Permalink
Browse files

[tex] more polishing

  • Loading branch information...
1 parent 579339b commit 968aa66d0f4a5156c97930f446fa27f0bfd5c302 @moritz committed Dec 17, 2009
View
BIN tex/adapting-pic.pdf
Binary file not shown.
View
473 tex/adapting.svg
@@ -28,15 +28,15 @@
inkscape:pageopacity="0.0"
inkscape:pageshadow="2"
inkscape:zoom="1.9294582"
- inkscape:cx="280.38956"
+ inkscape:cx="280.38955"
inkscape:cy="106.55677"
inkscape:document-units="px"
inkscape:current-layer="layer1"
showgrid="true"
inkscape:window-width="1156"
inkscape:window-height="670"
- inkscape:window-x="21"
- inkscape:window-y="111"
+ inkscape:window-x="20"
+ inkscape:window-y="92"
showguides="true"
inkscape:guide-bbox="true"
inkscape:snap-global="false">
@@ -162,138 +162,6 @@
-</g> <g
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
- ns0:text="\\begin{align*}\n\\mathbf{\\Psi_U^\\uparrow}\n\\end{align*}"
- word-spacing="normal"
- letter-spacing="normal"
- font-size-adjust="none"
- font-stretch="normal"
- font-weight="normal"
- font-variant="normal"
- font-style="normal"
- fill-rule="even-odd"
- stroke-miterlimit="10.433"
- xml:space="preserve"
- transform="matrix(1.6085256,0,0,-1.6085256,-482.98807,1366.2672)"
- id="content">
-<path
- style="fill:#000000;stroke-width:0"
- id="path2722"
- d="M 392.2,713.49 L 393.55,713.49 L 393.55,713.96 C 393.11,713.93 392.04,713.93 391.55,713.93 C 391.07,713.93 389.99,713.93 389.55,713.96 L 389.55,713.49 L 390.9,713.49 L 390.9,709.07 C 389.75,709.4 389.71,710.64 389.71,711.27 C 389.7,712.15 389.42,712.57 388.82,712.57 L 388.11,712.57 C 387.96,712.57 387.79,712.57 387.79,712.39 C 387.79,712.24 387.91,712.22 388.02,712.21 C 388.39,712.14 388.4,711.39 388.4,711.34 C 388.4,710.99 388.42,710.1 389,709.46 C 389.5,708.93 390.19,708.72 390.9,708.65 L 390.9,707.59 L 389.55,707.59 L 389.55,707.12 C 389.99,707.15 391.05,707.15 391.54,707.15 C 392.03,707.15 393.11,707.15 393.55,707.12 L 393.55,707.59 L 392.2,707.59 L 392.2,708.65 C 393.13,708.73 393.71,709.03 394.06,709.35 C 394.75,710 394.79,710.95 394.79,711.08 C 394.79,711.53 394.8,712.14 395.21,712.21 C 395.28,712.22 395.41,712.24 395.41,712.39 C 395.41,712.57 395.24,712.57 395.09,712.57 L 394.37,712.57 C 394.03,712.57 393.5,712.53 393.49,711.16 C 393.48,709.95 393.05,709.28 392.2,709.05 L 392.2,713.49 z" />
-<path
- style="fill:#000000;stroke-width:0"
- id="path2724"
- d="M 398.27,716.12 L 398.31,716.07 L 398.35,716.03 L 398.4,715.98 L 398.44,715.94 L 398.48,715.9 L 398.53,715.86 L 398.57,715.82 L 398.62,715.78 L 398.66,715.75 L 398.71,715.72 L 398.75,715.68 L 398.8,715.65 L 398.84,715.63 L 398.88,715.6 L 398.93,715.57 L 398.97,715.55 L 399.01,715.53 L 399.05,715.51 L 399.08,715.49 L 399.12,715.47 L 399.15,715.46 L 399.19,715.44 L 399.22,715.43 L 399.25,715.42 L 399.27,715.41 L 399.3,715.4 L 399.32,715.39 L 399.34,715.38 L 399.36,715.38 L 399.37,715.38 L 399.38,715.37 L 399.39,715.37 C 399.46,715.37 399.48,715.44 399.48,715.49 C 399.48,715.59 399.46,715.6 399.34,715.65 C 398.79,715.87 398.45,716.22 398.2,716.68 C 398.18,716.71 398.16,716.76 398.1,716.76 C 398.07,716.76 398.05,716.74 398.03,716.73 C 398.03,716.72 398.03,716.71 397.95,716.59 C 397.78,716.27 397.45,715.88 396.84,715.64 C 396.74,715.6 396.72,715.59 396.72,715.49 C 396.72,715.44 396.74,715.37 396.81,715.37 C 396.88,715.37 397.5,715.6 397.93,716.12 L 397.93,710.82 C 397.93,710.72 397.93,710.56 398.1,710.56 C 398.27,710.56 398.27,710.72 398.27,710.82 L 398.27,716.12 z" />
-<path
- style="fill:#000000;stroke-width:0"
- id="path2726"
- d="M 401.78,708.39 L 401.78,708.4 L 401.78,708.4 L 401.78,708.41 L 401.78,708.41 L 401.78,708.42 L 401.78,708.42 L 401.78,708.43 L 401.78,708.43 L 401.78,708.44 L 401.78,708.44 L 401.78,708.44 L 401.78,708.45 L 401.78,708.45 L 401.78,708.45 L 401.78,708.46 L 401.78,708.46 L 401.78,708.46 L 401.78,708.47 L 401.78,708.47 L 401.78,708.47 L 401.78,708.47 L 401.78,708.48 L 401.78,708.48 L 401.78,708.49 L 401.78,708.49 L 401.78,708.49 L 401.78,708.5 L 401.78,708.5 L 401.79,708.5 L 401.79,708.51 L 401.79,708.51 L 401.79,708.51 L 401.79,708.51 L 401.79,708.51 L 401.79,708.52 L 401.79,708.52 L 401.79,708.52 L 401.79,708.52 L 401.8,708.52 L 401.8,708.53 C 401.86,708.57 402.21,708.57 402.3,708.57 L 402.52,708.57 L 402.52,708.96 C 402.43,708.95 401.8,708.93 401.53,708.93 C 401.26,708.93 400.61,708.96 400.54,708.96 L 400.54,708.57 L 400.77,708.57 C 400.87,708.57 401.01,708.56 401.12,708.55 C 401.28,708.54 401.28,708.53 401.28,708.39 L 401.28,705.81 C 401.28,704.78 400.44,704.48 399.64,704.48 C 398.34,704.48 398.26,705.28 398.26,705.77 L 398.26,708.57 L 399,708.57 L 399,708.96 C 398.84,708.95 397.85,708.93 397.73,708.93 C 397.58,708.93 396.61,708.95 396.46,708.96 L 396.46,708.57 L 397.2,708.57 L 397.2,705.79 C 397.2,704.91 397.95,704.09 399.62,704.09 C 401.18,704.09 401.78,704.97 401.78,705.78 L 401.78,708.39 z" />
-</g> <g
- id="g2927"
- transform="matrix(1.6496158,0,0,-1.6496158,-434.06243,1380.7179)"
- xml:space="preserve"
- stroke-miterlimit="10.433"
- fill-rule="even-odd"
- font-style="normal"
- font-variant="normal"
- font-weight="normal"
- font-stretch="normal"
- font-size-adjust="none"
- letter-spacing="normal"
- word-spacing="normal"
- ns0:text="\\begin{align*}\n &amp;a \\mathbf{\\Psi^+_U}\\\\ \n+&amp; b \\mathbf{\\Psi^-_U}\n\\end{align*}"
- ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
-<path
- style="fill:#000000;stroke-width:0"
- d="M 392.1,710.89 L 392.09,710.92 L 392.07,710.96 L 392.05,710.99 L 392.03,711.02 L 392.01,711.05 L 391.99,711.08 L 391.97,711.11 L 391.95,711.14 L 391.93,711.17 L 391.9,711.2 L 391.88,711.23 L 391.85,711.25 L 391.83,711.28 L 391.8,711.3 L 391.77,711.32 L 391.75,711.35 L 391.72,711.37 L 391.69,711.39 L 391.66,711.4 L 391.63,711.42 L 391.59,711.44 L 391.56,711.45 L 391.53,711.47 L 391.49,711.48 L 391.46,711.49 L 391.42,711.5 L 391.39,711.51 L 391.35,711.51 L 391.31,711.52 L 391.27,711.52 L 391.23,711.53 L 391.19,711.53 L 391.2,711.31 C 391.85,711.31 391.98,710.49 391.98,710.43 C 391.98,710.37 391.96,710.31 391.95,710.26 L 391.46,708.31 C 391.41,708.13 391.41,708.11 391.26,707.94 C 390.82,707.39 390.41,707.23 390.13,707.23 C 389.63,707.23 389.49,707.78 389.49,708.17 C 389.49,708.67 389.81,709.89 390.04,710.35 C 390.35,710.94 390.8,711.31 391.2,711.31 L 391.19,711.53 C 390.02,711.53 388.79,710.06 388.79,708.61 C 388.79,707.67 389.33,707.01 390.11,707.01 C 390.31,707.01 390.81,707.05 391.41,707.76 C 391.49,707.34 391.83,707.01 392.31,707.01 C 392.66,707.01 392.89,707.24 393.05,707.56 C 393.22,707.92 393.35,708.53 393.35,708.55 C 393.35,708.65 393.26,708.65 393.23,708.65 C 393.13,708.65 393.12,708.61 393.09,708.47 C 392.92,707.82 392.74,707.23 392.33,707.23 C 392.06,707.23 392.03,707.49 392.03,707.69 C 392.03,707.91 392.05,707.99 392.16,708.43 C 392.27,708.85 392.29,708.95 392.38,709.32 C 392.55,709.96 392.59,710.15 392.74,710.72 C 392.81,711 392.81,711.02 392.81,711.06 C 392.81,711.23 392.69,711.33 392.52,711.33 C 392.28,711.33 392.13,711.11 392.1,710.89 z"
- id="path2929" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 398.7,713.49 L 400.05,713.49 L 400.05,713.96 C 399.61,713.93 398.54,713.93 398.06,713.93 C 397.57,713.93 396.49,713.93 396.05,713.96 L 396.05,713.49 L 397.4,713.49 L 397.4,709.07 C 396.25,709.4 396.21,710.64 396.21,711.27 C 396.2,712.15 395.92,712.57 395.33,712.57 L 394.61,712.57 C 394.46,712.57 394.29,712.57 394.29,712.39 C 394.29,712.24 394.41,712.22 394.52,712.21 C 394.9,712.14 394.91,711.39 394.91,711.34 C 394.91,710.99 394.92,710.1 395.51,709.46 C 396,708.93 396.69,708.72 397.4,708.65 L 397.4,707.59 L 396.05,707.59 L 396.05,707.12 C 396.49,707.15 397.56,707.15 398.05,707.15 C 398.53,707.15 399.61,707.15 400.05,707.12 L 400.05,707.59 L 398.7,707.59 L 398.7,708.65 C 399.63,708.73 400.22,709.03 400.57,709.35 C 401.25,710 401.29,710.95 401.29,711.08 C 401.29,711.53 401.3,712.14 401.71,712.21 C 401.78,712.22 401.91,712.24 401.91,712.39 C 401.91,712.57 401.74,712.57 401.59,712.57 L 400.88,712.57 C 400.54,712.57 400,712.53 399.99,711.16 C 399.98,709.95 399.55,709.28 398.7,709.05 L 398.7,713.49 z"
- id="path2931" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 405.8,712.97 L 407.93,712.97 C 408.02,712.97 408.19,712.97 408.19,713.13 C 408.19,713.31 408.03,713.31 407.93,713.31 L 405.8,713.31 L 405.8,715.45 C 405.8,715.54 405.8,715.71 405.63,715.71 C 405.46,715.71 405.46,715.55 405.46,715.45 L 405.46,713.31 L 403.32,713.31 C 403.23,713.31 403.06,713.31 403.06,713.14 C 403.06,712.97 403.22,712.97 403.32,712.97 L 405.46,712.97 L 405.46,710.83 C 405.46,710.73 405.46,710.57 405.62,710.57 C 405.8,710.57 405.8,710.73 405.8,710.83 L 405.8,712.97 z"
- id="path2933" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 408.29,708.39 L 408.29,708.4 L 408.29,708.4 L 408.29,708.41 L 408.29,708.41 L 408.29,708.42 L 408.29,708.42 L 408.29,708.43 L 408.29,708.43 L 408.29,708.44 L 408.29,708.44 L 408.29,708.44 L 408.29,708.45 L 408.29,708.45 L 408.29,708.45 L 408.29,708.46 L 408.29,708.46 L 408.29,708.46 L 408.29,708.47 L 408.29,708.47 L 408.29,708.47 L 408.29,708.47 L 408.29,708.48 L 408.29,708.48 L 408.29,708.49 L 408.29,708.49 L 408.29,708.49 L 408.29,708.5 L 408.29,708.5 L 408.3,708.5 L 408.3,708.51 L 408.3,708.51 L 408.3,708.51 L 408.3,708.51 L 408.3,708.51 L 408.3,708.52 L 408.3,708.52 L 408.3,708.52 L 408.3,708.52 L 408.31,708.52 L 408.31,708.53 C 408.37,708.57 408.72,708.57 408.8,708.57 L 409.04,708.57 L 409.04,708.96 C 408.94,708.95 408.31,708.93 408.04,708.93 C 407.77,708.93 407.12,708.96 407.05,708.96 L 407.05,708.57 L 407.28,708.57 C 407.38,708.57 407.52,708.56 407.63,708.55 C 407.79,708.54 407.79,708.53 407.79,708.39 L 407.79,705.81 C 407.79,704.78 406.95,704.48 406.15,704.48 C 404.85,704.48 404.77,705.28 404.77,705.77 L 404.77,708.57 L 405.51,708.57 L 405.51,708.96 C 405.35,708.95 404.36,708.93 404.24,708.93 C 404.09,708.93 403.12,708.95 402.97,708.96 L 402.97,708.57 L 403.71,708.57 L 403.71,705.79 C 403.71,704.91 404.46,704.09 406.13,704.09 C 407.69,704.09 408.29,704.97 408.29,705.78 L 408.29,708.39 z"
- id="path2935" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 384.71,693.27 L 387.49,693.27 C 387.63,693.27 387.82,693.27 387.82,693.47 C 387.82,693.66 387.63,693.66 387.49,693.66 L 384.71,693.66 L 384.71,696.45 C 384.71,696.59 384.71,696.78 384.52,696.78 C 384.32,696.78 384.32,696.59 384.32,696.45 L 384.32,693.66 L 381.53,693.66 C 381.39,693.66 381.2,693.66 381.2,693.47 C 381.2,693.27 381.39,693.27 381.53,693.27 L 384.32,693.27 L 384.32,690.48 C 384.32,690.34 384.32,690.15 384.52,690.15 C 384.71,690.15 384.71,690.34 384.71,690.48 L 384.71,693.27 z"
- id="path2937" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 390.77,697.78 L 390.77,697.78 L 390.77,697.78 L 390.77,697.78 L 390.77,697.78 L 390.77,697.79 L 390.77,697.79 L 390.77,697.79 L 390.77,697.8 L 390.77,697.8 L 390.77,697.8 L 390.77,697.81 L 390.76,697.81 L 390.76,697.82 L 390.76,697.82 L 390.76,697.83 L 390.76,697.83 L 390.75,697.84 L 390.75,697.84 L 390.75,697.85 L 390.74,697.85 L 390.74,697.86 L 390.73,697.86 L 390.73,697.86 L 390.73,697.86 L 390.73,697.87 L 390.72,697.87 L 390.72,697.87 L 390.72,697.87 L 390.71,697.87 L 390.71,697.87 L 390.71,697.88 L 390.7,697.88 L 390.7,697.88 L 390.7,697.88 L 390.69,697.88 L 390.69,697.88 L 390.68,697.88 L 390.68,697.89 L 390.67,697.89 L 390.67,697.89 L 390.66,697.89 L 390.66,697.89 L 390.65,697.89 L 390.65,697.89 L 390.64,697.89 C 390.41,697.89 389.68,697.81 389.42,697.79 C 389.34,697.78 389.23,697.77 389.23,697.59 C 389.23,697.47 389.32,697.47 389.47,697.47 C 389.95,697.47 389.97,697.4 389.97,697.3 C 389.97,697.23 389.88,696.89 389.83,696.68 L 389.02,693.44 C 388.9,692.94 388.86,692.78 388.86,692.43 C 388.86,691.48 389.38,690.86 390.12,690.86 C 391.3,690.86 392.52,692.35 392.52,693.78 C 392.52,694.69 391.99,695.38 391.2,695.38 L 391.18,695.16 C 391.54,695.16 391.8,694.86 391.8,694.22 C 391.8,693.64 391.48,692.49 391.3,692.11 C 390.97,691.44 390.51,691.09 390.12,691.09 C 389.78,691.09 389.45,691.35 389.45,692.09 C 389.45,692.28 389.45,692.47 389.61,693.1 L 389.83,694.01 C 389.89,694.23 389.89,694.25 389.98,694.36 C 390.47,695.01 390.92,695.16 391.18,695.16 L 391.2,695.38 C 390.74,695.38 390.33,695.09 390.03,694.78 L 390.77,697.78 z"
- id="path2939" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 397.71,697.34 L 399.06,697.34 L 399.06,697.81 C 398.62,697.78 397.55,697.78 397.07,697.78 C 396.58,697.78 395.5,697.78 395.06,697.81 L 395.06,697.34 L 396.41,697.34 L 396.41,692.92 C 395.26,693.26 395.22,694.49 395.22,695.12 C 395.21,696.01 394.93,696.42 394.34,696.42 L 393.62,696.42 C 393.47,696.42 393.3,696.42 393.3,696.24 C 393.3,696.1 393.42,696.08 393.53,696.07 C 393.91,696 393.92,695.24 393.92,695.19 C 393.92,694.84 393.93,693.95 394.52,693.32 C 395.01,692.78 395.7,692.57 396.41,692.5 L 396.41,691.44 L 395.06,691.44 L 395.06,690.97 C 395.5,691.01 396.57,691.01 397.06,691.01 C 397.54,691.01 398.62,691.01 399.06,690.97 L 399.06,691.44 L 397.71,691.44 L 397.71,692.5 C 398.64,692.58 399.23,692.89 399.58,693.21 C 400.26,693.85 400.3,694.8 400.3,694.93 C 400.3,695.38 400.31,696 400.72,696.07 C 400.79,696.08 400.92,696.1 400.92,696.24 C 400.92,696.42 400.75,696.42 400.6,696.42 L 399.89,696.42 C 399.55,696.42 399.01,696.39 399,695.01 C 398.99,693.8 398.56,693.14 397.71,692.91 L 397.71,697.34 z"
- id="path2941" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 406.79,696.81 L 406.8,696.81 L 406.81,696.81 L 406.82,696.81 L 406.83,696.81 L 406.84,696.81 L 406.85,696.81 L 406.86,696.81 L 406.87,696.81 L 406.88,696.81 L 406.89,696.82 L 406.9,696.82 L 406.91,696.82 L 406.92,696.82 L 406.93,696.82 L 406.94,696.83 L 406.95,696.83 L 406.96,696.84 L 406.97,696.84 L 406.98,696.85 L 406.99,696.85 L 407,696.86 L 407.01,696.87 L 407.01,696.87 L 407.02,696.88 L 407.02,696.88 L 407.02,696.89 L 407.03,696.89 L 407.03,696.9 L 407.03,696.9 L 407.03,696.91 L 407.04,696.91 L 407.04,696.92 L 407.04,696.92 L 407.04,696.93 L 407.04,696.94 L 407.04,696.94 L 407.05,696.95 L 407.05,696.96 L 407.05,696.96 L 407.05,696.97 L 407.05,696.98 C 407.05,697.15 406.89,697.15 406.79,697.15 L 402.59,697.15 C 402.49,697.15 402.33,697.15 402.33,696.98 C 402.33,696.81 402.5,696.81 402.59,696.81 L 406.79,696.81 z"
- id="path2943" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 407.3,692.25 L 407.3,692.25 L 407.3,692.26 L 407.3,692.26 L 407.3,692.27 L 407.3,692.27 L 407.3,692.28 L 407.3,692.28 L 407.3,692.28 L 407.3,692.29 L 407.3,692.29 L 407.3,692.3 L 407.3,692.3 L 407.3,692.3 L 407.3,692.31 L 407.3,692.31 L 407.3,692.31 L 407.3,692.32 L 407.3,692.32 L 407.3,692.32 L 407.3,692.32 L 407.3,692.33 L 407.3,692.33 L 407.3,692.33 L 407.3,692.34 L 407.3,692.34 L 407.3,692.35 L 407.3,692.35 L 407.3,692.35 L 407.31,692.36 L 407.31,692.36 L 407.31,692.36 L 407.31,692.36 L 407.31,692.36 L 407.31,692.37 L 407.31,692.37 L 407.31,692.37 L 407.31,692.37 L 407.31,692.37 L 407.32,692.38 L 407.32,692.38 C 407.38,692.42 407.73,692.42 407.82,692.42 L 408.05,692.42 L 408.05,692.81 C 407.95,692.8 407.32,692.78 407.05,692.78 C 406.78,692.78 406.13,692.81 406.06,692.81 L 406.06,692.42 L 406.29,692.42 C 406.39,692.42 406.53,692.41 406.64,692.41 C 406.8,692.39 406.8,692.39 406.8,692.25 L 406.8,689.66 C 406.8,688.63 405.96,688.33 405.17,688.33 C 403.86,688.33 403.78,689.13 403.78,689.62 L 403.78,692.42 L 404.52,692.42 L 404.52,692.81 C 404.36,692.8 403.36,692.78 403.25,692.78 C 403.1,692.78 402.13,692.8 401.98,692.81 L 401.98,692.42 L 402.72,692.42 L 402.72,689.64 C 402.72,688.77 403.47,687.94 405.14,687.94 C 406.7,687.94 407.3,688.82 407.3,689.63 L 407.3,692.25 z"
- id="path2945" />
-</g> <g
- id="g3129"
- transform="matrix(1.6496158,0,0,-1.6496158,-217.6447,1380.7179)"
- xml:space="preserve"
- stroke-miterlimit="10.433"
- fill-rule="even-odd"
- font-style="normal"
- font-variant="normal"
- font-weight="normal"
- font-stretch="normal"
- font-size-adjust="none"
- letter-spacing="normal"
- word-spacing="normal"
- ns0:text="\\begin{align*}\n &amp;a \\mathbf{\\Psi^+_U}\\\\ \n+&amp; b \\mathbf{\\Psi^-_U}\n\\end{align*}"
- ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
-<path
- style="fill:#000000;stroke-width:0"
- d="M 392.1,710.89 L 392.09,710.92 L 392.07,710.96 L 392.05,710.99 L 392.03,711.02 L 392.01,711.05 L 391.99,711.08 L 391.97,711.11 L 391.95,711.14 L 391.93,711.17 L 391.9,711.2 L 391.88,711.23 L 391.85,711.25 L 391.83,711.28 L 391.8,711.3 L 391.77,711.32 L 391.75,711.35 L 391.72,711.37 L 391.69,711.39 L 391.66,711.4 L 391.63,711.42 L 391.59,711.44 L 391.56,711.45 L 391.53,711.47 L 391.49,711.48 L 391.46,711.49 L 391.42,711.5 L 391.39,711.51 L 391.35,711.51 L 391.31,711.52 L 391.27,711.52 L 391.23,711.53 L 391.19,711.53 L 391.2,711.31 C 391.85,711.31 391.98,710.49 391.98,710.43 C 391.98,710.37 391.96,710.31 391.95,710.26 L 391.46,708.31 C 391.41,708.13 391.41,708.11 391.26,707.94 C 390.82,707.39 390.41,707.23 390.13,707.23 C 389.63,707.23 389.49,707.78 389.49,708.17 C 389.49,708.67 389.81,709.89 390.04,710.35 C 390.35,710.94 390.8,711.31 391.2,711.31 L 391.19,711.53 C 390.02,711.53 388.79,710.06 388.79,708.61 C 388.79,707.67 389.33,707.01 390.11,707.01 C 390.31,707.01 390.81,707.05 391.41,707.76 C 391.49,707.34 391.83,707.01 392.31,707.01 C 392.66,707.01 392.89,707.24 393.05,707.56 C 393.22,707.92 393.35,708.53 393.35,708.55 C 393.35,708.65 393.26,708.65 393.23,708.65 C 393.13,708.65 393.12,708.61 393.09,708.47 C 392.92,707.82 392.74,707.23 392.33,707.23 C 392.06,707.23 392.03,707.49 392.03,707.69 C 392.03,707.91 392.05,707.99 392.16,708.43 C 392.27,708.85 392.29,708.95 392.38,709.32 C 392.55,709.96 392.59,710.15 392.74,710.72 C 392.81,711 392.81,711.02 392.81,711.06 C 392.81,711.23 392.69,711.33 392.52,711.33 C 392.28,711.33 392.13,711.11 392.1,710.89 z"
- id="path3131" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 398.7,713.49 L 400.05,713.49 L 400.05,713.96 C 399.61,713.93 398.54,713.93 398.06,713.93 C 397.57,713.93 396.49,713.93 396.05,713.96 L 396.05,713.49 L 397.4,713.49 L 397.4,709.07 C 396.25,709.4 396.21,710.64 396.21,711.27 C 396.2,712.15 395.92,712.57 395.33,712.57 L 394.61,712.57 C 394.46,712.57 394.29,712.57 394.29,712.39 C 394.29,712.24 394.41,712.22 394.52,712.21 C 394.9,712.14 394.91,711.39 394.91,711.34 C 394.91,710.99 394.92,710.1 395.51,709.46 C 396,708.93 396.69,708.72 397.4,708.65 L 397.4,707.59 L 396.05,707.59 L 396.05,707.12 C 396.49,707.15 397.56,707.15 398.05,707.15 C 398.53,707.15 399.61,707.15 400.05,707.12 L 400.05,707.59 L 398.7,707.59 L 398.7,708.65 C 399.63,708.73 400.22,709.03 400.57,709.35 C 401.25,710 401.29,710.95 401.29,711.08 C 401.29,711.53 401.3,712.14 401.71,712.21 C 401.78,712.22 401.91,712.24 401.91,712.39 C 401.91,712.57 401.74,712.57 401.59,712.57 L 400.88,712.57 C 400.54,712.57 400,712.53 399.99,711.16 C 399.98,709.95 399.55,709.28 398.7,709.05 L 398.7,713.49 z"
- id="path3133" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 405.8,712.97 L 407.93,712.97 C 408.02,712.97 408.19,712.97 408.19,713.13 C 408.19,713.31 408.03,713.31 407.93,713.31 L 405.8,713.31 L 405.8,715.45 C 405.8,715.54 405.8,715.71 405.63,715.71 C 405.46,715.71 405.46,715.55 405.46,715.45 L 405.46,713.31 L 403.32,713.31 C 403.23,713.31 403.06,713.31 403.06,713.14 C 403.06,712.97 403.22,712.97 403.32,712.97 L 405.46,712.97 L 405.46,710.83 C 405.46,710.73 405.46,710.57 405.62,710.57 C 405.8,710.57 405.8,710.73 405.8,710.83 L 405.8,712.97 z"
- id="path3135" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 408.29,708.39 L 408.29,708.4 L 408.29,708.4 L 408.29,708.41 L 408.29,708.41 L 408.29,708.42 L 408.29,708.42 L 408.29,708.43 L 408.29,708.43 L 408.29,708.44 L 408.29,708.44 L 408.29,708.44 L 408.29,708.45 L 408.29,708.45 L 408.29,708.45 L 408.29,708.46 L 408.29,708.46 L 408.29,708.46 L 408.29,708.47 L 408.29,708.47 L 408.29,708.47 L 408.29,708.47 L 408.29,708.48 L 408.29,708.48 L 408.29,708.49 L 408.29,708.49 L 408.29,708.49 L 408.29,708.5 L 408.29,708.5 L 408.3,708.5 L 408.3,708.51 L 408.3,708.51 L 408.3,708.51 L 408.3,708.51 L 408.3,708.51 L 408.3,708.52 L 408.3,708.52 L 408.3,708.52 L 408.3,708.52 L 408.31,708.52 L 408.31,708.53 C 408.37,708.57 408.72,708.57 408.8,708.57 L 409.04,708.57 L 409.04,708.96 C 408.94,708.95 408.31,708.93 408.04,708.93 C 407.77,708.93 407.12,708.96 407.05,708.96 L 407.05,708.57 L 407.28,708.57 C 407.38,708.57 407.52,708.56 407.63,708.55 C 407.79,708.54 407.79,708.53 407.79,708.39 L 407.79,705.81 C 407.79,704.78 406.95,704.48 406.15,704.48 C 404.85,704.48 404.77,705.28 404.77,705.77 L 404.77,708.57 L 405.51,708.57 L 405.51,708.96 C 405.35,708.95 404.36,708.93 404.24,708.93 C 404.09,708.93 403.12,708.95 402.97,708.96 L 402.97,708.57 L 403.71,708.57 L 403.71,705.79 C 403.71,704.91 404.46,704.09 406.13,704.09 C 407.69,704.09 408.29,704.97 408.29,705.78 L 408.29,708.39 z"
- id="path3137" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 384.71,693.27 L 387.49,693.27 C 387.63,693.27 387.82,693.27 387.82,693.47 C 387.82,693.66 387.63,693.66 387.49,693.66 L 384.71,693.66 L 384.71,696.45 C 384.71,696.59 384.71,696.78 384.52,696.78 C 384.32,696.78 384.32,696.59 384.32,696.45 L 384.32,693.66 L 381.53,693.66 C 381.39,693.66 381.2,693.66 381.2,693.47 C 381.2,693.27 381.39,693.27 381.53,693.27 L 384.32,693.27 L 384.32,690.48 C 384.32,690.34 384.32,690.15 384.52,690.15 C 384.71,690.15 384.71,690.34 384.71,690.48 L 384.71,693.27 z"
- id="path3139" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 390.77,697.78 L 390.77,697.78 L 390.77,697.78 L 390.77,697.78 L 390.77,697.78 L 390.77,697.79 L 390.77,697.79 L 390.77,697.79 L 390.77,697.8 L 390.77,697.8 L 390.77,697.8 L 390.77,697.81 L 390.76,697.81 L 390.76,697.82 L 390.76,697.82 L 390.76,697.83 L 390.76,697.83 L 390.75,697.84 L 390.75,697.84 L 390.75,697.85 L 390.74,697.85 L 390.74,697.86 L 390.73,697.86 L 390.73,697.86 L 390.73,697.86 L 390.73,697.87 L 390.72,697.87 L 390.72,697.87 L 390.72,697.87 L 390.71,697.87 L 390.71,697.87 L 390.71,697.88 L 390.7,697.88 L 390.7,697.88 L 390.7,697.88 L 390.69,697.88 L 390.69,697.88 L 390.68,697.88 L 390.68,697.89 L 390.67,697.89 L 390.67,697.89 L 390.66,697.89 L 390.66,697.89 L 390.65,697.89 L 390.65,697.89 L 390.64,697.89 C 390.41,697.89 389.68,697.81 389.42,697.79 C 389.34,697.78 389.23,697.77 389.23,697.59 C 389.23,697.47 389.32,697.47 389.47,697.47 C 389.95,697.47 389.97,697.4 389.97,697.3 C 389.97,697.23 389.88,696.89 389.83,696.68 L 389.02,693.44 C 388.9,692.94 388.86,692.78 388.86,692.43 C 388.86,691.48 389.38,690.86 390.12,690.86 C 391.3,690.86 392.52,692.35 392.52,693.78 C 392.52,694.69 391.99,695.38 391.2,695.38 L 391.18,695.16 C 391.54,695.16 391.8,694.86 391.8,694.22 C 391.8,693.64 391.48,692.49 391.3,692.11 C 390.97,691.44 390.51,691.09 390.12,691.09 C 389.78,691.09 389.45,691.35 389.45,692.09 C 389.45,692.28 389.45,692.47 389.61,693.1 L 389.83,694.01 C 389.89,694.23 389.89,694.25 389.98,694.36 C 390.47,695.01 390.92,695.16 391.18,695.16 L 391.2,695.38 C 390.74,695.38 390.33,695.09 390.03,694.78 L 390.77,697.78 z"
- id="path3141" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 397.71,697.34 L 399.06,697.34 L 399.06,697.81 C 398.62,697.78 397.55,697.78 397.07,697.78 C 396.58,697.78 395.5,697.78 395.06,697.81 L 395.06,697.34 L 396.41,697.34 L 396.41,692.92 C 395.26,693.26 395.22,694.49 395.22,695.12 C 395.21,696.01 394.93,696.42 394.34,696.42 L 393.62,696.42 C 393.47,696.42 393.3,696.42 393.3,696.24 C 393.3,696.1 393.42,696.08 393.53,696.07 C 393.91,696 393.92,695.24 393.92,695.19 C 393.92,694.84 393.93,693.95 394.52,693.32 C 395.01,692.78 395.7,692.57 396.41,692.5 L 396.41,691.44 L 395.06,691.44 L 395.06,690.97 C 395.5,691.01 396.57,691.01 397.06,691.01 C 397.54,691.01 398.62,691.01 399.06,690.97 L 399.06,691.44 L 397.71,691.44 L 397.71,692.5 C 398.64,692.58 399.23,692.89 399.58,693.21 C 400.26,693.85 400.3,694.8 400.3,694.93 C 400.3,695.38 400.31,696 400.72,696.07 C 400.79,696.08 400.92,696.1 400.92,696.24 C 400.92,696.42 400.75,696.42 400.6,696.42 L 399.89,696.42 C 399.55,696.42 399.01,696.39 399,695.01 C 398.99,693.8 398.56,693.14 397.71,692.91 L 397.71,697.34 z"
- id="path3143" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 406.79,696.81 L 406.8,696.81 L 406.81,696.81 L 406.82,696.81 L 406.83,696.81 L 406.84,696.81 L 406.85,696.81 L 406.86,696.81 L 406.87,696.81 L 406.88,696.81 L 406.89,696.82 L 406.9,696.82 L 406.91,696.82 L 406.92,696.82 L 406.93,696.82 L 406.94,696.83 L 406.95,696.83 L 406.96,696.84 L 406.97,696.84 L 406.98,696.85 L 406.99,696.85 L 407,696.86 L 407.01,696.87 L 407.01,696.87 L 407.02,696.88 L 407.02,696.88 L 407.02,696.89 L 407.03,696.89 L 407.03,696.9 L 407.03,696.9 L 407.03,696.91 L 407.04,696.91 L 407.04,696.92 L 407.04,696.92 L 407.04,696.93 L 407.04,696.94 L 407.04,696.94 L 407.05,696.95 L 407.05,696.96 L 407.05,696.96 L 407.05,696.97 L 407.05,696.98 C 407.05,697.15 406.89,697.15 406.79,697.15 L 402.59,697.15 C 402.49,697.15 402.33,697.15 402.33,696.98 C 402.33,696.81 402.5,696.81 402.59,696.81 L 406.79,696.81 z"
- id="path3145" />
-<path
- style="fill:#000000;stroke-width:0"
- d="M 407.3,692.25 L 407.3,692.25 L 407.3,692.26 L 407.3,692.26 L 407.3,692.27 L 407.3,692.27 L 407.3,692.28 L 407.3,692.28 L 407.3,692.28 L 407.3,692.29 L 407.3,692.29 L 407.3,692.3 L 407.3,692.3 L 407.3,692.3 L 407.3,692.31 L 407.3,692.31 L 407.3,692.31 L 407.3,692.32 L 407.3,692.32 L 407.3,692.32 L 407.3,692.32 L 407.3,692.33 L 407.3,692.33 L 407.3,692.33 L 407.3,692.34 L 407.3,692.34 L 407.3,692.35 L 407.3,692.35 L 407.3,692.35 L 407.31,692.36 L 407.31,692.36 L 407.31,692.36 L 407.31,692.36 L 407.31,692.36 L 407.31,692.37 L 407.31,692.37 L 407.31,692.37 L 407.31,692.37 L 407.31,692.37 L 407.32,692.38 L 407.32,692.38 C 407.38,692.42 407.73,692.42 407.82,692.42 L 408.05,692.42 L 408.05,692.81 C 407.95,692.8 407.32,692.78 407.05,692.78 C 406.78,692.78 406.13,692.81 406.06,692.81 L 406.06,692.42 L 406.29,692.42 C 406.39,692.42 406.53,692.41 406.64,692.41 C 406.8,692.39 406.8,692.39 406.8,692.25 L 406.8,689.66 C 406.8,688.63 405.96,688.33 405.17,688.33 C 403.86,688.33 403.78,689.13 403.78,689.62 L 403.78,692.42 L 404.52,692.42 L 404.52,692.81 C 404.36,692.8 403.36,692.78 403.25,692.78 C 403.1,692.78 402.13,692.8 401.98,692.81 L 401.98,692.42 L 402.72,692.42 L 402.72,689.64 C 402.72,688.77 403.47,687.94 405.14,687.94 C 406.7,687.94 407.3,688.82 407.3,689.63 L 407.3,692.25 z"
- id="path3147" />
</g> <path
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;marker-end:url(#Arrow1Lend);stroke-opacity:1"
d="M 49.490432,292.48835 L 589.76686,292.48835"
@@ -326,97 +194,7 @@
id="path4969"
d="M 469.99676,285.0436 L 469.99676,299.9331"
style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1" />
- <g
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
- ns0:text="\\begin{align*}\n&amp;\\sqrt{T_{\\uparrow\\uparrow}}\\mathbf{\\Psi_U^\\uparrow}\\\\\n+&amp;\\sqrt{T_{\\downarrow\\uparrow}}\\mathbf{\\Psi_U^\\downarrow}\n\\end{align*}"
- word-spacing="normal"
- letter-spacing="normal"
- font-size-adjust="none"
- font-stretch="normal"
- font-weight="normal"
- font-variant="normal"
- font-style="normal"
- fill-rule="even-odd"
- stroke-miterlimit="10.433"
- xml:space="preserve"
- transform="matrix(1.6085256,0,0,-1.6085256,-121.67076,1351.2203)"
- id="g5304">
-<path
- id="path5306"
- d="M 383.03,704.06 L 383.04,704.06 L 383.06,704.06 L 383.07,704.06 L 383.08,704.06 L 383.09,704.06 L 383.11,704.06 L 383.12,704.06 L 383.13,704.06 L 383.14,704.06 L 383.15,704.06 L 383.16,704.06 L 383.17,704.07 L 383.19,704.07 L 383.21,704.07 L 383.23,704.07 L 383.24,704.07 L 383.26,704.07 L 383.27,704.08 L 383.28,704.08 L 383.29,704.08 L 383.3,704.09 L 383.31,704.09 L 383.32,704.1 L 383.33,704.1 L 383.34,704.11 L 383.35,704.12 L 383.36,704.12 L 383.37,704.13 L 383.37,704.14 L 383.38,704.15 L 383.39,704.16 L 383.4,704.17 L 383.4,704.19 L 383.41,704.2 L 383.42,704.21 L 383.43,704.23 L 383.44,704.25 L 383.45,704.26 L 388.89,715.64 C 388.96,715.77 388.96,715.79 388.96,715.82 C 388.96,715.93 388.89,716.02 388.77,716.02 C 388.64,716.02 388.6,715.93 388.55,715.82 L 383.4,705.1 L 381.28,710.04 L 379.9,708.97 L 380.05,708.82 L 380.76,709.35 L 383.03,704.06 z"
- style="fill:#000000;stroke-width:0" />
-<line
- id="line5308"
- y2="715.82001"
- x2="403.25"
- y1="715.82001"
- x1="388.76001"
- style="stroke-width:0.398" />
-<path
- id="path5310"
- d="M 393.02,713.17 L 393.02,713.2 L 393.03,713.22 L 393.04,713.24 L 393.04,713.26 L 393.05,713.29 L 393.05,713.31 L 393.06,713.32 L 393.07,713.34 L 393.07,713.36 L 393.08,713.37 L 393.08,713.39 L 393.09,713.4 L 393.09,713.41 L 393.1,713.43 L 393.11,713.44 L 393.11,713.45 L 393.12,713.46 L 393.13,713.47 L 393.13,713.47 L 393.14,713.48 L 393.15,713.49 L 393.15,713.5 L 393.16,713.5 L 393.17,713.51 L 393.18,713.51 L 393.19,713.52 L 393.2,713.52 L 393.2,713.53 L 393.21,713.53 L 393.22,713.53 L 393.23,713.54 L 393.25,713.54 C 393.33,713.56 393.66,713.56 393.87,713.56 C 394.88,713.56 395.33,713.52 395.33,712.74 C 395.33,712.59 395.29,712.2 395.25,711.94 C 395.24,711.91 395.22,711.78 395.22,711.76 C 395.22,711.7 395.25,711.63 395.34,711.63 C 395.45,711.63 395.47,711.71 395.49,711.85 L 395.76,713.59 C 395.77,713.63 395.78,713.73 395.78,713.76 C 395.78,713.87 395.68,713.87 395.51,713.87 L 389.98,713.87 C 389.74,713.87 389.73,713.86 389.66,713.67 L 389.06,711.91 C 389.05,711.9 389,711.76 389,711.73 C 389,711.67 389.05,711.63 389.12,711.63 C 389.22,711.63 389.23,711.67 389.29,711.84 C 389.83,713.38 390.09,713.56 391.56,713.56 L 391.95,713.56 C 392.23,713.56 392.23,713.52 392.23,713.44 C 392.23,713.38 392.2,713.26 392.19,713.23 L 390.86,707.91 C 390.77,707.54 390.73,707.43 389.67,707.43 C 389.31,707.43 389.25,707.43 389.25,707.24 C 389.25,707.12 389.36,707.12 389.42,707.12 C 389.69,707.12 389.97,707.14 390.24,707.14 C 390.52,707.14 390.8,707.15 391.08,707.15 C 391.36,707.15 391.64,707.14 391.91,707.14 C 392.2,707.14 392.5,707.12 392.78,707.12 C 392.88,707.12 393,707.12 393,707.32 C 393,707.43 392.92,707.43 392.66,707.43 C 392.41,707.43 392.28,707.43 392.02,707.45 C 391.73,707.48 391.65,707.51 391.65,707.67 C 391.65,707.68 391.65,707.73 391.69,707.88 L 393.02,713.17 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5312"
- d="M 396.79,709.84 L 396.83,709.79 L 396.88,709.74 L 396.92,709.7 L 396.96,709.65 L 397.01,709.61 L 397.05,709.57 L 397.1,709.53 L 397.14,709.5 L 397.19,709.46 L 397.23,709.43 L 397.28,709.4 L 397.32,709.37 L 397.36,709.34 L 397.41,709.31 L 397.45,709.29 L 397.49,709.27 L 397.53,709.24 L 397.57,709.22 L 397.61,709.2 L 397.64,709.19 L 397.68,709.17 L 397.71,709.16 L 397.74,709.14 L 397.77,709.13 L 397.8,709.12 L 397.82,709.11 L 397.84,709.11 L 397.86,709.1 L 397.88,709.09 L 397.89,709.09 L 397.9,709.09 L 397.91,709.09 C 397.98,709.09 398.01,709.15 398.01,709.21 C 398.01,709.3 397.99,709.31 397.86,709.36 C 397.31,709.58 396.97,709.93 396.72,710.39 C 396.7,710.43 396.68,710.47 396.63,710.47 C 396.59,710.47 396.58,710.46 396.56,710.44 C 396.55,710.43 396.55,710.43 396.47,710.3 C 396.3,709.98 395.97,709.6 395.36,709.35 C 395.26,709.31 395.24,709.3 395.24,709.21 C 395.24,709.15 395.26,709.09 395.34,709.09 C 395.4,709.09 396.02,709.31 396.45,709.84 L 396.45,704.53 C 396.45,704.44 396.45,704.28 396.62,704.28 C 396.79,704.28 396.79,704.43 396.79,704.53 L 396.79,709.84 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5314"
- d="M 400.87,709.84 L 400.91,709.79 L 400.96,709.74 L 401,709.7 L 401.04,709.65 L 401.09,709.61 L 401.13,709.57 L 401.18,709.53 L 401.22,709.5 L 401.27,709.46 L 401.31,709.43 L 401.36,709.4 L 401.4,709.37 L 401.44,709.34 L 401.49,709.31 L 401.53,709.29 L 401.57,709.27 L 401.61,709.24 L 401.65,709.22 L 401.69,709.2 L 401.72,709.19 L 401.76,709.17 L 401.79,709.16 L 401.82,709.14 L 401.85,709.13 L 401.88,709.12 L 401.9,709.11 L 401.92,709.11 L 401.94,709.1 L 401.96,709.09 L 401.97,709.09 L 401.98,709.09 L 401.99,709.09 C 402.06,709.09 402.09,709.15 402.09,709.21 C 402.09,709.3 402.07,709.31 401.94,709.36 C 401.39,709.58 401.05,709.93 400.8,710.39 C 400.78,710.43 400.76,710.47 400.71,710.47 C 400.67,710.47 400.66,710.46 400.64,710.44 C 400.63,710.43 400.63,710.43 400.55,710.3 C 400.38,709.98 400.05,709.6 399.44,709.35 C 399.34,709.31 399.32,709.3 399.32,709.21 C 399.32,709.15 399.34,709.09 399.42,709.09 C 399.48,709.09 400.1,709.31 400.53,709.84 L 400.53,704.53 C 400.53,704.44 400.53,704.28 400.7,704.28 C 400.87,704.28 400.87,704.43 400.87,704.53 L 400.87,709.84 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5316"
- d="M 408.3,713.49 L 409.64,713.49 L 409.64,713.96 C 409.2,713.93 408.14,713.93 407.65,713.93 C 407.16,713.93 406.08,713.93 405.65,713.96 L 405.65,713.49 L 406.99,713.49 L 406.99,709.07 C 405.85,709.4 405.8,710.64 405.8,711.27 C 405.8,712.15 405.52,712.57 404.92,712.57 L 404.2,712.57 C 404.05,712.57 403.88,712.57 403.88,712.39 C 403.88,712.24 404,712.22 404.11,712.21 C 404.49,712.14 404.5,711.39 404.5,711.34 C 404.5,710.99 404.51,710.1 405.1,709.46 C 405.6,708.93 406.28,708.72 406.99,708.65 L 406.99,707.59 L 405.65,707.59 L 405.65,707.12 C 406.08,707.15 407.15,707.15 407.64,707.15 C 408.13,707.15 409.2,707.15 409.64,707.12 L 409.64,707.59 L 408.3,707.59 L 408.3,708.65 C 409.22,708.73 409.81,709.03 410.16,709.35 C 410.85,710 410.89,710.95 410.89,711.08 C 410.89,711.53 410.9,712.14 411.3,712.21 C 411.37,712.22 411.5,712.24 411.5,712.39 C 411.5,712.57 411.33,712.57 411.18,712.57 L 410.47,712.57 C 410.13,712.57 409.59,712.53 409.58,711.16 C 409.57,709.95 409.14,709.28 408.3,709.05 L 408.3,713.49 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5318"
- d="M 414.37,716.12 L 414.41,716.07 L 414.45,716.03 L 414.49,715.98 L 414.54,715.94 L 414.58,715.9 L 414.62,715.86 L 414.67,715.82 L 414.71,715.78 L 414.76,715.75 L 414.8,715.72 L 414.85,715.68 L 414.89,715.65 L 414.94,715.63 L 414.98,715.6 L 415.02,715.57 L 415.06,715.55 L 415.1,715.53 L 415.14,715.51 L 415.18,715.49 L 415.22,715.47 L 415.25,715.46 L 415.28,715.44 L 415.31,715.43 L 415.34,715.42 L 415.37,715.41 L 415.39,715.4 L 415.41,715.39 L 415.43,715.38 L 415.45,715.38 L 415.46,715.38 L 415.47,715.37 L 415.48,715.37 C 415.55,715.37 415.58,715.44 415.58,715.49 C 415.58,715.59 415.56,715.6 415.43,715.65 C 414.88,715.87 414.54,716.22 414.3,716.68 C 414.27,716.71 414.25,716.76 414.2,716.76 C 414.16,716.76 414.15,716.74 414.13,716.73 C 414.12,716.72 414.12,716.71 414.05,716.59 C 413.87,716.27 413.54,715.88 412.94,715.64 C 412.83,715.6 412.81,715.59 412.81,715.49 C 412.81,715.44 412.83,715.37 412.91,715.37 C 412.97,715.37 413.59,715.6 414.02,716.12 L 414.02,710.82 C 414.02,710.72 414.02,710.56 414.19,710.56 C 414.37,710.56 414.37,710.72 414.37,710.82 L 414.37,716.12 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5320"
- d="M 417.87,708.39 L 417.87,708.4 L 417.87,708.4 L 417.87,708.41 L 417.87,708.41 L 417.87,708.42 L 417.87,708.42 L 417.87,708.43 L 417.87,708.43 L 417.87,708.44 L 417.87,708.44 L 417.87,708.44 L 417.87,708.45 L 417.87,708.45 L 417.87,708.45 L 417.88,708.46 L 417.88,708.46 L 417.88,708.46 L 417.88,708.47 L 417.88,708.47 L 417.88,708.47 L 417.88,708.47 L 417.88,708.48 L 417.88,708.48 L 417.88,708.49 L 417.88,708.49 L 417.88,708.49 L 417.88,708.5 L 417.88,708.5 L 417.88,708.5 L 417.88,708.51 L 417.88,708.51 L 417.88,708.51 L 417.88,708.51 L 417.88,708.51 L 417.88,708.52 L 417.89,708.52 L 417.89,708.52 L 417.89,708.52 L 417.89,708.52 L 417.89,708.53 C 417.96,708.57 418.31,708.57 418.39,708.57 L 418.62,708.57 L 418.62,708.96 C 418.53,708.95 417.89,708.93 417.63,708.93 C 417.36,708.93 416.7,708.96 416.63,708.96 L 416.63,708.57 L 416.86,708.57 C 416.97,708.57 417.11,708.56 417.21,708.55 C 417.37,708.54 417.38,708.53 417.38,708.39 L 417.38,705.81 C 417.38,704.78 416.54,704.48 415.74,704.48 C 414.43,704.48 414.35,705.28 414.35,705.77 L 414.35,708.57 L 415.1,708.57 L 415.1,708.96 C 414.94,708.95 413.94,708.93 413.83,708.93 C 413.67,708.93 412.71,708.95 412.55,708.96 L 412.55,708.57 L 413.3,708.57 L 413.3,705.79 C 413.3,704.91 414.05,704.09 415.71,704.09 C 417.27,704.09 417.87,704.97 417.87,705.78 L 417.87,708.39 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5322"
- d="M 375.12,692.22 L 377.9,692.22 C 378.04,692.22 378.23,692.22 378.23,692.42 C 378.23,692.61 378.04,692.61 377.9,692.61 L 375.12,692.61 L 375.12,695.4 C 375.12,695.54 375.12,695.73 374.92,695.73 C 374.72,695.73 374.72,695.54 374.72,695.4 L 374.72,692.61 L 371.93,692.61 C 371.8,692.61 371.61,692.61 371.61,692.42 C 371.61,692.22 371.8,692.22 371.93,692.22 L 374.72,692.22 L 374.72,689.43 C 374.72,689.29 374.72,689.1 374.92,689.1 C 375.12,689.1 375.12,689.29 375.12,689.43 L 375.12,692.22 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5324"
- d="M 383.03,686.86 L 383.04,686.86 L 383.06,686.86 L 383.07,686.86 L 383.08,686.86 L 383.09,686.86 L 383.11,686.86 L 383.12,686.86 L 383.13,686.86 L 383.14,686.86 L 383.15,686.86 L 383.16,686.86 L 383.17,686.86 L 383.19,686.86 L 383.21,686.86 L 383.23,686.86 L 383.24,686.87 L 383.26,686.87 L 383.27,686.87 L 383.28,686.87 L 383.29,686.88 L 383.3,686.88 L 383.31,686.89 L 383.32,686.89 L 383.33,686.9 L 383.34,686.9 L 383.35,686.91 L 383.36,686.92 L 383.37,686.93 L 383.37,686.94 L 383.38,686.95 L 383.39,686.96 L 383.4,686.97 L 383.4,686.98 L 383.41,686.99 L 383.42,687.01 L 383.43,687.02 L 383.44,687.04 L 383.45,687.06 L 388.89,698.43 C 388.96,698.56 388.96,698.58 388.96,698.61 C 388.96,698.72 388.89,698.81 388.77,698.81 C 388.64,698.81 388.6,698.72 388.55,698.61 L 383.4,687.9 L 381.28,692.84 L 379.9,691.77 L 380.05,691.61 L 380.76,692.15 L 383.03,686.86 z"
- style="fill:#000000;stroke-width:0" />
-<line
- id="line5326"
- y2="698.60999"
- x2="403.25"
- y1="698.60999"
- x1="388.76001"
- style="stroke-width:0.398" />
-<path
- id="path5328"
- d="M 393.02,695.97 L 393.02,696 L 393.03,696.02 L 393.04,696.04 L 393.04,696.07 L 393.05,696.09 L 393.05,696.11 L 393.06,696.13 L 393.07,696.14 L 393.07,696.16 L 393.08,696.18 L 393.08,696.19 L 393.09,696.2 L 393.09,696.22 L 393.1,696.23 L 393.11,696.24 L 393.11,696.25 L 393.12,696.26 L 393.13,696.27 L 393.13,696.28 L 393.14,696.28 L 393.15,696.29 L 393.15,696.3 L 393.16,696.3 L 393.17,696.31 L 393.18,696.32 L 393.19,696.32 L 393.2,696.32 L 393.2,696.33 L 393.21,696.33 L 393.22,696.33 L 393.23,696.34 L 393.25,696.34 C 393.33,696.36 393.66,696.36 393.87,696.36 C 394.88,696.36 395.33,696.32 395.33,695.54 C 395.33,695.39 395.29,695.01 395.25,694.75 C 395.24,694.71 395.22,694.59 395.22,694.56 C 395.22,694.5 395.25,694.43 395.34,694.43 C 395.45,694.43 395.47,694.51 395.49,694.66 L 395.76,696.39 C 395.77,696.43 395.78,696.53 395.78,696.56 C 395.78,696.67 395.68,696.67 395.51,696.67 L 389.98,696.67 C 389.74,696.67 389.73,696.66 389.66,696.47 L 389.06,694.72 C 389.05,694.7 389,694.56 389,694.54 C 389,694.48 389.05,694.43 389.12,694.43 C 389.22,694.43 389.23,694.48 389.29,694.64 C 389.83,696.18 390.09,696.36 391.56,696.36 L 391.95,696.36 C 392.23,696.36 392.23,696.32 392.23,696.24 C 392.23,696.18 392.2,696.06 392.19,696.03 L 390.86,690.71 C 390.77,690.34 390.73,690.23 389.67,690.23 C 389.31,690.23 389.25,690.23 389.25,690.04 C 389.25,689.92 389.36,689.92 389.42,689.92 C 389.69,689.92 389.97,689.95 390.24,689.95 C 390.52,689.95 390.8,689.96 391.08,689.96 C 391.36,689.96 391.64,689.95 391.91,689.95 C 392.2,689.95 392.5,689.92 392.78,689.92 C 392.88,689.92 393,689.92 393,690.12 C 393,690.23 392.92,690.23 392.66,690.23 C 392.41,690.23 392.28,690.23 392.02,690.25 C 391.73,690.28 391.65,690.31 391.65,690.47 C 391.65,690.48 391.65,690.53 391.69,690.68 L 393.02,695.97 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5330"
- d="M 396.79,693.01 L 396.79,693.02 L 396.79,693.03 L 396.79,693.04 L 396.79,693.05 L 396.79,693.06 L 396.79,693.07 L 396.79,693.08 L 396.79,693.1 L 396.79,693.11 L 396.79,693.12 L 396.79,693.13 L 396.78,693.14 L 396.78,693.15 L 396.78,693.16 L 396.78,693.17 L 396.77,693.18 L 396.77,693.19 L 396.76,693.2 L 396.76,693.21 L 396.75,693.22 L 396.75,693.22 L 396.74,693.23 L 396.73,693.24 L 396.73,693.24 L 396.72,693.25 L 396.72,693.25 L 396.71,693.25 L 396.71,693.25 L 396.7,693.26 L 396.7,693.26 L 396.69,693.26 L 396.69,693.26 L 396.68,693.26 L 396.68,693.27 L 396.67,693.27 L 396.66,693.27 L 396.66,693.27 L 396.65,693.27 L 396.64,693.27 L 396.63,693.27 L 396.63,693.27 C 396.45,693.27 396.45,693.12 396.45,693.01 L 396.45,687.71 C 396.02,688.24 395.4,688.46 395.34,688.46 C 395.27,688.46 395.24,688.4 395.24,688.34 C 395.24,688.24 395.26,688.24 395.38,688.19 C 395.89,687.99 396.26,687.64 396.49,687.21 C 396.56,687.1 396.56,687.08 396.63,687.08 C 396.68,687.08 396.7,687.11 396.75,687.21 C 397.09,687.84 397.6,688.08 397.88,688.2 C 397.99,688.24 398.01,688.24 398.01,688.34 C 398.01,688.4 397.99,688.46 397.91,688.46 C 397.85,688.46 397.23,688.24 396.79,687.71 L 396.79,693.01 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5332"
- d="M 400.87,692.64 L 400.91,692.59 L 400.96,692.54 L 401,692.5 L 401.04,692.46 L 401.09,692.41 L 401.13,692.37 L 401.18,692.34 L 401.22,692.3 L 401.27,692.27 L 401.31,692.23 L 401.36,692.2 L 401.4,692.17 L 401.44,692.14 L 401.49,692.12 L 401.53,692.09 L 401.57,692.07 L 401.61,692.05 L 401.65,692.03 L 401.69,692.01 L 401.72,691.99 L 401.76,691.97 L 401.79,691.96 L 401.82,691.95 L 401.85,691.94 L 401.88,691.92 L 401.9,691.92 L 401.92,691.91 L 401.94,691.9 L 401.96,691.9 L 401.97,691.89 L 401.98,691.89 L 401.99,691.89 C 402.06,691.89 402.09,691.95 402.09,692.01 C 402.09,692.11 402.07,692.11 401.94,692.16 C 401.39,692.39 401.05,692.73 400.8,693.2 C 400.78,693.23 400.76,693.27 400.71,693.27 C 400.67,693.27 400.66,693.26 400.64,693.24 C 400.63,693.24 400.63,693.23 400.55,693.1 C 400.38,692.78 400.05,692.4 399.44,692.16 C 399.34,692.11 399.32,692.11 399.32,692.01 C 399.32,691.95 399.34,691.89 399.42,691.89 C 399.48,691.89 400.1,692.11 400.53,692.64 L 400.53,687.34 C 400.53,687.24 400.53,687.08 400.7,687.08 C 400.87,687.08 400.87,687.23 400.87,687.34 L 400.87,692.64 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5334"
- d="M 408.3,696.29 L 409.64,696.29 L 409.64,696.76 C 409.2,696.73 408.14,696.73 407.65,696.73 C 407.16,696.73 406.08,696.73 405.65,696.76 L 405.65,696.29 L 406.99,696.29 L 406.99,691.87 C 405.85,692.21 405.8,693.44 405.8,694.07 C 405.8,694.96 405.52,695.38 404.92,695.38 L 404.2,695.38 C 404.05,695.38 403.88,695.38 403.88,695.2 C 403.88,695.05 404,695.03 404.11,695.02 C 404.49,694.95 404.5,694.19 404.5,694.14 C 404.5,693.79 404.51,692.9 405.1,692.27 C 405.6,691.73 406.28,691.52 406.99,691.45 L 406.99,690.39 L 405.65,690.39 L 405.65,689.92 C 406.08,689.96 407.15,689.96 407.64,689.96 C 408.13,689.96 409.2,689.96 409.64,689.92 L 409.64,690.39 L 408.3,690.39 L 408.3,691.45 C 409.22,691.53 409.81,691.84 410.16,692.16 C 410.85,692.8 410.89,693.75 410.89,693.88 C 410.89,694.33 410.9,694.95 411.3,695.02 C 411.37,695.03 411.5,695.05 411.5,695.2 C 411.5,695.38 411.33,695.38 411.18,695.38 L 410.47,695.38 C 410.13,695.38 409.59,695.34 409.58,693.96 C 409.57,692.75 409.14,692.09 408.3,691.86 L 408.3,696.29 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5336"
- d="M 414.37,699.29 L 414.37,699.3 L 414.37,699.31 L 414.37,699.32 L 414.37,699.33 L 414.37,699.34 L 414.36,699.35 L 414.36,699.36 L 414.36,699.37 L 414.36,699.38 L 414.36,699.39 L 414.36,699.41 L 414.36,699.42 L 414.35,699.43 L 414.35,699.44 L 414.35,699.45 L 414.34,699.46 L 414.34,699.47 L 414.34,699.48 L 414.33,699.49 L 414.32,699.49 L 414.32,699.5 L 414.31,699.51 L 414.3,699.52 L 414.3,699.52 L 414.3,699.52 L 414.29,699.53 L 414.29,699.53 L 414.28,699.53 L 414.28,699.53 L 414.27,699.54 L 414.27,699.54 L 414.26,699.54 L 414.25,699.54 L 414.25,699.54 L 414.24,699.55 L 414.23,699.55 L 414.23,699.55 L 414.22,699.55 L 414.21,699.55 L 414.21,699.55 L 414.2,699.55 C 414.02,699.55 414.02,699.4 414.02,699.29 L 414.02,693.99 C 413.59,694.52 412.97,694.74 412.91,694.74 C 412.84,694.74 412.81,694.67 412.81,694.62 C 412.81,694.52 412.83,694.52 412.96,694.47 C 413.47,694.26 413.83,693.92 414.07,693.49 C 414.13,693.38 414.14,693.36 414.2,693.36 C 414.25,693.36 414.27,693.39 414.32,693.48 C 414.66,694.12 415.17,694.36 415.45,694.47 C 415.56,694.52 415.58,694.52 415.58,694.62 C 415.58,694.67 415.56,694.74 415.48,694.74 C 415.42,694.74 414.8,694.52 414.37,693.99 L 414.37,699.29 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path5338"
- d="M 417.87,691.2 L 417.87,691.2 L 417.87,691.21 L 417.87,691.21 L 417.87,691.22 L 417.87,691.22 L 417.87,691.23 L 417.87,691.23 L 417.87,691.23 L 417.87,691.24 L 417.87,691.24 L 417.87,691.25 L 417.87,691.25 L 417.87,691.25 L 417.87,691.26 L 417.88,691.26 L 417.88,691.26 L 417.88,691.27 L 417.88,691.27 L 417.88,691.27 L 417.88,691.27 L 417.88,691.28 L 417.88,691.28 L 417.88,691.28 L 417.88,691.29 L 417.88,691.29 L 417.88,691.3 L 417.88,691.3 L 417.88,691.3 L 417.88,691.31 L 417.88,691.31 L 417.88,691.31 L 417.88,691.31 L 417.88,691.31 L 417.88,691.32 L 417.88,691.32 L 417.89,691.32 L 417.89,691.32 L 417.89,691.32 L 417.89,691.33 L 417.89,691.33 C 417.96,691.37 418.31,691.37 418.39,691.37 L 418.62,691.37 L 418.62,691.76 C 418.53,691.76 417.89,691.73 417.63,691.73 C 417.36,691.73 416.7,691.76 416.63,691.76 L 416.63,691.37 L 416.86,691.37 C 416.97,691.37 417.11,691.36 417.21,691.36 C 417.37,691.34 417.38,691.34 417.38,691.2 L 417.38,688.61 C 417.38,687.58 416.54,687.28 415.74,687.28 C 414.43,687.28 414.35,688.08 414.35,688.57 L 414.35,691.37 L 415.1,691.37 L 415.1,691.76 C 414.94,691.75 413.94,691.73 413.83,691.73 C 413.67,691.73 412.71,691.75 412.55,691.76 L 412.55,691.37 L 413.3,691.37 L 413.3,688.59 C 413.3,687.72 414.05,686.89 415.71,686.89 C 417.27,686.89 417.87,687.77 417.87,688.58 L 417.87,691.2 z"
- style="fill:#000000;stroke-width:0" />
-</g> <text
+ <text
xml:space="preserve"
style="font-size:20px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
x="287.7793"
@@ -506,6 +284,249 @@
fill="black"
stroke-width="0"
d="M232.65,706.9 H232.41 C232.39,706.75,232.32,706.33,232.23,706.27 C232.17,706.22,231.64,706.22,231.54,706.22 H230.26 C230.99,706.87,231.23,707.07,231.65,707.39 C232.17,707.81,232.65,708.24,232.65,708.9 C232.65,709.74,231.91,710.26,231.01,710.26 C230.15,710.26,229.56,709.65,229.56,709.01 C229.56,708.66,229.86,708.62,229.93,708.62 C230.1,708.62,230.3,708.74,230.3,708.99 C230.3,709.12,230.26,709.36,229.89,709.36 C230.11,709.86,230.58,710.01,230.91,710.01 C231.61,710.01,231.97,709.47,231.97,708.9 C231.97,708.29,231.54,707.81,231.32,707.56 L229.63,705.9 C229.56,705.84,229.56,705.83,229.56,705.63 H232.44 Z " />
+</g> <g
+ id="content"
+ transform="matrix(1.6085256,0,0,-1.6085256,-482.98807,1366.2672)"
+ xml:space="preserve"
+ stroke="black"
+ stroke-linecap="butt"
+ stroke-linejoin="miter"
+ stroke-miterlimit="10.433"
+ stroke-dasharray="none"
+ stroke-dashoffset="0"
+ stroke-opacity="1"
+ fill="none"
+ fill-rule="even-odd"
+ fill-opacity="1"
+ font-style="normal"
+ font-variant="normal"
+ font-weight="normal"
+ font-stretch="normal"
+ font-size-adjust="none"
+ letter-spacing="normal"
+ word-spacing="normal"
+ text-anchor="start"
+ ns0:text="\\begin{align*}\n\\mathbf{\\Psi^\\uparrow}\n\\end{align*}"
+ ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
+<path
+ d="M393.6,713.49 H394.94 V713.96 C394.5,713.93,393.44,713.93,392.95,713.93 C392.46,713.93,391.38,713.93,390.95,713.96 V713.49 H392.29 V709.07 C391.14,709.4,391.11,710.64,391.11,711.27 C391.1,712.15,390.82,712.57,390.22,712.57 H389.5 C389.35,712.57,389.18,712.57,389.18,712.39 C389.18,712.24,389.3,712.22,389.41,712.21 C389.79,712.14,389.8,711.39,389.8,711.34 C389.8,710.99,389.81,710.1,390.4,709.46 C390.9,708.93,391.58,708.72,392.29,708.65 V707.59 H390.95 V707.12 C391.38,707.15,392.45,707.15,392.94,707.15 C393.43,707.15,394.5,707.15,394.94,707.12 V707.59 H393.6 V708.65 C394.52,708.73,395.11,709.03,395.46,709.35 C396.15,710,396.19,710.95,396.19,711.08 C396.19,711.53,396.2,712.14,396.61,712.21 C396.67,712.22,396.8,712.24,396.8,712.39 C396.8,712.57,396.64,712.57,396.48,712.57 H395.77 C395.43,712.57,394.89,712.53,394.88,711.16 C394.87,709.95,394.44,709.28,393.6,709.05 Z "
+ stroke-width="0"
+ fill="black"
+ id="path2518" />
+<path
+ d="M399.67,715.45 L399.71,715.4 L399.75,715.35 L399.79,715.31 L399.84,715.26 L399.88,715.22 L399.92,715.18 L399.97,715.14 L400.01,715.11 L400.06,715.07 L400.1,715.04 L400.15,715.01 L400.19,714.98 L400.24,714.95 L400.28,714.92 L400.32,714.9 L400.36,714.88 L400.4,714.85 L400.44,714.83 L400.48,714.81 L400.52,714.8 L400.55,714.78 L400.58,714.77 L400.61,714.75 L400.64,714.74 L400.67,714.73 L400.69,714.72 L400.71,714.72 L400.73,714.71 L400.75,714.7 L400.76,714.7 L400.77,714.7 L400.78,714.7 C400.85,714.7,400.88,714.76,400.88,714.82 C400.88,714.91,400.86,714.92,400.73,714.97 C400.18,715.19,399.84,715.54,399.6,716 C399.58,716.04,399.55,716.08,399.5,716.08 C399.46,716.08,399.45,716.07,399.43,716.05 C399.42,716.04,399.42,716.04,399.35,715.91 C399.17,715.59,398.84,715.21,398.24,714.96 C398.13,714.92,398.11,714.91,398.11,714.82 C398.11,714.76,398.13,714.7,398.21,714.7 C398.27,714.7,398.89,714.92,399.32,715.45 V710.15 C399.32,710.05,399.32,709.89,399.49,709.89 C399.67,709.89,399.67,710.04,399.67,710.15 Z "
+ stroke-width="0"
+ fill="black"
+ id="path2521" />
+</g> <g
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
+ ns0:text="\\begin{align*}\n &amp;a \\mathbf{\\Psi^+}\\\\ \n+&amp; b \\mathbf{\\Psi^-}\n\\end{align*}"
+ text-anchor="start"
+ word-spacing="normal"
+ letter-spacing="normal"
+ font-size-adjust="none"
+ font-stretch="normal"
+ font-weight="normal"
+ font-variant="normal"
+ font-style="normal"
+ fill-opacity="1"
+ fill-rule="even-odd"
+ fill="none"
+ stroke-opacity="1"
+ stroke-dashoffset="0"
+ stroke-dasharray="none"
+ stroke-miterlimit="10.433"
+ stroke-linejoin="miter"
+ stroke-linecap="butt"
+ stroke="black"
+ xml:space="preserve"
+ transform="matrix(1.6496158,0,0,-1.6496158,-434.06243,1380.7179)"
+ id="g2663">
+<path
+ id="path2665"
+ fill="black"
+ stroke-width="0"
+ d="M392.48,710.89 L392.46,710.92 L392.44,710.96 L392.43,710.99 L392.41,711.02 L392.39,711.05 L392.37,711.08 L392.34,711.11 L392.32,711.14 L392.3,711.17 L392.28,711.2 L392.25,711.23 L392.23,711.25 L392.2,711.28 L392.18,711.3 L392.15,711.32 L392.12,711.35 L392.09,711.37 L392.06,711.39 L392.03,711.4 L392,711.42 L391.97,711.44 L391.94,711.45 L391.9,711.47 L391.87,711.48 L391.83,711.49 L391.8,711.5 L391.76,711.51 L391.72,711.51 L391.68,711.52 L391.64,711.52 L391.6,711.53 L391.56,711.53 L391.57,711.31 C392.22,711.31,392.36,710.49,392.36,710.43 C392.36,710.37,392.34,710.31,392.33,710.26 L391.83,708.31 C391.78,708.13,391.78,708.11,391.63,707.94 C391.19,707.39,390.79,707.23,390.51,707.23 C390.01,707.23,389.87,707.78,389.87,708.17 C389.87,708.67,390.19,709.89,390.42,710.35 C390.73,710.94,391.17,711.31,391.57,711.31 L391.56,711.53 C390.4,711.53,389.16,710.06,389.16,708.61 C389.16,707.67,389.71,707.01,390.49,707.01 C390.68,707.01,391.18,707.05,391.78,707.76 C391.86,707.34,392.21,707.01,392.69,707.01 C393.04,707.01,393.27,707.24,393.42,707.56 C393.59,707.92,393.72,708.53,393.72,708.55 C393.72,708.65,393.63,708.65,393.6,708.65 C393.51,708.65,393.49,708.61,393.46,708.47 C393.3,707.82,393.12,707.23,392.71,707.23 C392.44,707.23,392.41,707.49,392.41,707.69 C392.41,707.91,392.43,707.99,392.54,708.43 C392.65,708.85,392.67,708.95,392.76,709.32 C392.93,709.96,392.97,710.15,393.12,710.72 C393.19,711,393.19,711.02,393.19,711.06 C393.19,711.23,393.07,711.33,392.9,711.33 C392.66,711.33,392.51,711.11,392.48,710.89 Z " />
+<path
+ id="path2667"
+ fill="black"
+ stroke-width="0"
+ d="M399.09,713.49 H400.43 V713.96 C399.99,713.93,398.93,713.93,398.44,713.93 C397.95,713.93,396.87,713.93,396.44,713.96 V713.49 H397.78 V709.07 C396.64,709.4,396.6,710.64,396.6,711.27 C396.58,712.15,396.31,712.57,395.71,712.57 H394.99 C394.84,712.57,394.67,712.57,394.67,712.39 C394.67,712.24,394.79,712.22,394.9,712.21 C395.28,712.14,395.29,711.39,395.29,711.34 C395.29,710.99,395.3,710.1,395.89,709.46 C396.39,708.93,397.07,708.72,397.78,708.65 V707.59 H396.44 V707.12 C396.87,707.15,397.94,707.15,398.43,707.15 C398.92,707.15,399.99,707.15,400.43,707.12 V707.59 H399.09 V708.65 C400.01,708.73,400.6,709.03,400.95,709.35 C401.64,710,401.68,710.95,401.68,711.08 C401.68,711.53,401.69,712.14,402.1,712.21 C402.16,712.22,402.29,712.24,402.29,712.39 C402.29,712.57,402.12,712.57,401.98,712.57 H401.26 C400.92,712.57,400.38,712.53,400.37,711.16 C400.36,709.95,399.93,709.28,399.09,709.05 Z " />
+<path
+ id="path2669"
+ fill="black"
+ stroke-width="0"
+ d="M406.17,712.82 H408.31 C408.4,712.82,408.57,712.82,408.57,712.98 C408.57,713.16,408.41,713.16,408.31,713.16 H406.17 V715.3 C406.17,715.39,406.17,715.56,406.01,715.56 C405.83,715.56,405.83,715.4,405.83,715.3 V713.16 H403.69 C403.6,713.16,403.43,713.16,403.43,712.99 C403.43,712.82,403.59,712.82,403.69,712.82 H405.83 V710.67 C405.83,710.58,405.83,710.42,406,710.42 C406.17,710.42,406.17,710.58,406.17,710.67 Z " />
+<path
+ id="path2671"
+ fill="black"
+ stroke-width="0"
+ d="M385.09,693.42 H387.87 C388.01,693.42,388.2,693.42,388.2,693.62 C388.2,693.82,388.01,693.82,387.87,693.82 H385.09 V696.6 C385.09,696.74,385.09,696.93,384.89,696.93 C384.69,696.93,384.69,696.74,384.69,696.6 V693.82 H381.9 C381.76,693.82,381.57,693.82,381.57,693.62 C381.57,693.42,381.76,693.42,381.9,693.42 H384.69 V690.63 C384.69,690.49,384.69,690.3,384.89,690.3 C385.09,690.3,385.09,690.49,385.09,690.63 Z " />
+<path
+ id="path2673"
+ fill="black"
+ stroke-width="0"
+ d="M391.14,697.93 L391.14,697.93 L391.14,697.93 L391.14,697.93 L391.14,697.93 L391.14,697.94 L391.14,697.94 L391.14,697.94 L391.14,697.95 L391.14,697.95 L391.14,697.95 L391.14,697.96 L391.14,697.96 L391.14,697.97 L391.14,697.97 L391.13,697.98 L391.13,697.98 L391.13,697.99 L391.12,697.99 L391.12,698 L391.12,698 L391.11,698.01 L391.11,698.01 L391.11,698.01 L391.1,698.01 L391.1,698.02 L391.1,698.02 L391.1,698.02 L391.09,698.02 L391.09,698.02 L391.09,698.02 L391.08,698.03 L391.08,698.03 L391.07,698.03 L391.07,698.03 L391.07,698.03 L391.06,698.03 L391.06,698.03 L391.05,698.04 L391.05,698.04 L391.04,698.04 L391.04,698.04 L391.03,698.04 L391.03,698.04 L391.02,698.04 L391.01,698.04 C390.79,698.04,390.06,697.96,389.8,697.94 C389.72,697.93,389.61,697.92,389.61,697.74 C389.61,697.62,389.7,697.62,389.85,697.62 C390.33,697.62,390.35,697.55,390.35,697.45 C390.35,697.38,390.26,697.04,390.21,696.83 L389.39,693.59 C389.27,693.09,389.23,692.93,389.23,692.58 C389.23,691.63,389.76,691.02,390.5,691.02 V691.23 C390.16,691.23,389.83,691.5,389.83,692.24 C389.83,692.43,389.83,692.62,389.99,693.25 L390.21,694.16 C390.27,694.38,390.27,694.4,390.36,694.51 C390.85,695.16,391.29,695.31,391.55,695.31 C391.91,695.31,392.18,695.01,392.18,694.37 C392.18,693.78,391.85,692.64,391.67,692.26 C391.34,691.59,390.89,691.23,390.5,691.23 V691.02 C391.67,691.02,392.9,692.5,392.9,693.93 C392.9,694.84,392.37,695.53,391.57,695.53 C391.11,695.53,390.7,695.24,390.41,694.93 Z " />
+<path
+ id="path2676"
+ fill="black"
+ stroke-width="0"
+ d="M398.1,697.49 H399.44 V697.96 C399,697.93,397.94,697.93,397.45,697.93 C396.96,697.93,395.88,697.93,395.45,697.96 V697.49 H396.79 V693.07 C395.64,693.41,395.61,694.64,395.61,695.27 C395.6,696.16,395.32,696.58,394.72,696.58 H394 C393.85,696.58,393.68,696.58,393.68,696.4 C393.68,696.25,393.8,696.23,393.91,696.22 C394.29,696.15,394.3,695.39,394.3,695.34 C394.3,694.99,394.31,694.1,394.9,693.47 C395.4,692.93,396.08,692.72,396.79,692.65 V691.59 H395.45 V691.12 C395.88,691.16,396.95,691.16,397.44,691.16 C397.93,691.16,399,691.16,399.44,691.12 V691.59 H398.1 V692.65 C399.02,692.73,399.61,693.04,399.96,693.36 C400.65,694,400.69,694.95,400.69,695.08 C400.69,695.53,400.7,696.15,401.11,696.22 C401.17,696.23,401.3,696.25,401.3,696.4 C401.3,696.58,401.14,696.58,400.98,696.58 H400.27 C399.93,696.58,399.39,696.53,399.38,695.16 C399.37,693.95,398.94,693.29,398.1,693.06 Z " />
+<path
+ id="path2678"
+ fill="black"
+ stroke-width="0"
+ d="M407.16,696.81 L407.17,696.81 L407.18,696.81 L407.19,696.81 L407.2,696.81 L407.21,696.81 L407.22,696.81 L407.23,696.81 L407.24,696.81 L407.25,696.81 L407.26,696.82 L407.27,696.82 L407.29,696.82 L407.3,696.82 L407.31,696.82 L407.32,696.83 L407.33,696.83 L407.34,696.84 L407.35,696.84 L407.36,696.85 L407.36,696.85 L407.37,696.86 L407.38,696.87 L407.39,696.87 L407.39,696.88 L407.39,696.88 L407.4,696.89 L407.4,696.89 L407.4,696.9 L407.41,696.9 L407.41,696.91 L407.41,696.91 L407.41,696.92 L407.41,696.92 L407.42,696.93 L407.42,696.94 L407.42,696.94 L407.42,696.95 L407.42,696.96 L407.42,696.96 L407.42,696.97 L407.42,696.98 C407.42,697.15,407.26,697.15,407.16,697.15 H402.97 C402.87,697.15,402.71,697.15,402.71,696.98 C402.71,696.81,402.88,696.81,402.97,696.81 Z " />
+</g> <g
+ id="g2816"
+ transform="matrix(1.6496158,0,0,-1.6496158,-218.68126,1380.7179)"
+ xml:space="preserve"
+ stroke-miterlimit="10.433"
+ fill-rule="even-odd"
+ font-style="normal"
+ font-variant="normal"
+ font-weight="normal"
+ font-stretch="normal"
+ font-size-adjust="none"
+ letter-spacing="normal"
+ word-spacing="normal"
+ ns0:text="\\begin{align*}\n &amp;a \\mathbf{\\Psi^+}\\\\ \n+&amp; b \\mathbf{\\Psi^-}\n\\end{align*}"
+ ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
+<path
+ style="fill:#000000;stroke-width:0"
+ d="M 392.48,710.89 L 392.46,710.92 L 392.44,710.96 L 392.43,710.99 L 392.41,711.02 L 392.39,711.05 L 392.37,711.08 L 392.34,711.11 L 392.32,711.14 L 392.3,711.17 L 392.28,711.2 L 392.25,711.23 L 392.23,711.25 L 392.2,711.28 L 392.18,711.3 L 392.15,711.32 L 392.12,711.35 L 392.09,711.37 L 392.06,711.39 L 392.03,711.4 L 392,711.42 L 391.97,711.44 L 391.94,711.45 L 391.9,711.47 L 391.87,711.48 L 391.83,711.49 L 391.8,711.5 L 391.76,711.51 L 391.72,711.51 L 391.68,711.52 L 391.64,711.52 L 391.6,711.53 L 391.56,711.53 L 391.57,711.31 C 392.22,711.31 392.36,710.49 392.36,710.43 C 392.36,710.37 392.34,710.31 392.33,710.26 L 391.83,708.31 C 391.78,708.13 391.78,708.11 391.63,707.94 C 391.19,707.39 390.79,707.23 390.51,707.23 C 390.01,707.23 389.87,707.78 389.87,708.17 C 389.87,708.67 390.19,709.89 390.42,710.35 C 390.73,710.94 391.17,711.31 391.57,711.31 L 391.56,711.53 C 390.4,711.53 389.16,710.06 389.16,708.61 C 389.16,707.67 389.71,707.01 390.49,707.01 C 390.68,707.01 391.18,707.05 391.78,707.76 C 391.86,707.34 392.21,707.01 392.69,707.01 C 393.04,707.01 393.27,707.24 393.42,707.56 C 393.59,707.92 393.72,708.53 393.72,708.55 C 393.72,708.65 393.63,708.65 393.6,708.65 C 393.51,708.65 393.49,708.61 393.46,708.47 C 393.3,707.82 393.12,707.23 392.71,707.23 C 392.44,707.23 392.41,707.49 392.41,707.69 C 392.41,707.91 392.43,707.99 392.54,708.43 C 392.65,708.85 392.67,708.95 392.76,709.32 C 392.93,709.96 392.97,710.15 393.12,710.72 C 393.19,711 393.19,711.02 393.19,711.06 C 393.19,711.23 393.07,711.33 392.9,711.33 C 392.66,711.33 392.51,711.11 392.48,710.89 z"
+ id="path2818" />
+<path
+ style="fill:#000000;stroke-width:0"
+ d="M 399.09,713.49 L 400.43,713.49 L 400.43,713.96 C 399.99,713.93 398.93,713.93 398.44,713.93 C 397.95,713.93 396.87,713.93 396.44,713.96 L 396.44,713.49 L 397.78,713.49 L 397.78,709.07 C 396.64,709.4 396.6,710.64 396.6,711.27 C 396.58,712.15 396.31,712.57 395.71,712.57 L 394.99,712.57 C 394.84,712.57 394.67,712.57 394.67,712.39 C 394.67,712.24 394.79,712.22 394.9,712.21 C 395.28,712.14 395.29,711.39 395.29,711.34 C 395.29,710.99 395.3,710.1 395.89,709.46 C 396.39,708.93 397.07,708.72 397.78,708.65 L 397.78,707.59 L 396.44,707.59 L 396.44,707.12 C 396.87,707.15 397.94,707.15 398.43,707.15 C 398.92,707.15 399.99,707.15 400.43,707.12 L 400.43,707.59 L 399.09,707.59 L 399.09,708.65 C 400.01,708.73 400.6,709.03 400.95,709.35 C 401.64,710 401.68,710.95 401.68,711.08 C 401.68,711.53 401.69,712.14 402.1,712.21 C 402.16,712.22 402.29,712.24 402.29,712.39 C 402.29,712.57 402.12,712.57 401.98,712.57 L 401.26,712.57 C 400.92,712.57 400.38,712.53 400.37,711.16 C 400.36,709.95 399.93,709.28 399.09,709.05 L 399.09,713.49 z"
+ id="path2820" />
+<path
+ style="fill:#000000;stroke-width:0"
+ d="M 406.17,712.82 L 408.31,712.82 C 408.4,712.82 408.57,712.82 408.57,712.98 C 408.57,713.16 408.41,713.16 408.31,713.16 L 406.17,713.16 L 406.17,715.3 C 406.17,715.39 406.17,715.56 406.01,715.56 C 405.83,715.56 405.83,715.4 405.83,715.3 L 405.83,713.16 L 403.69,713.16 C 403.6,713.16 403.43,713.16 403.43,712.99 C 403.43,712.82 403.59,712.82 403.69,712.82 L 405.83,712.82 L 405.83,710.67 C 405.83,710.58 405.83,710.42 406,710.42 C 406.17,710.42 406.17,710.58 406.17,710.67 L 406.17,712.82 z"
+ id="path2822" />
+<path
+ style="fill:#000000;stroke-width:0"
+ d="M 385.09,693.42 L 387.87,693.42 C 388.01,693.42 388.2,693.42 388.2,693.62 C 388.2,693.82 388.01,693.82 387.87,693.82 L 385.09,693.82 L 385.09,696.6 C 385.09,696.74 385.09,696.93 384.89,696.93 C 384.69,696.93 384.69,696.74 384.69,696.6 L 384.69,693.82 L 381.9,693.82 C 381.76,693.82 381.57,693.82 381.57,693.62 C 381.57,693.42 381.76,693.42 381.9,693.42 L 384.69,693.42 L 384.69,690.63 C 384.69,690.49 384.69,690.3 384.89,690.3 C 385.09,690.3 385.09,690.49 385.09,690.63 L 385.09,693.42 z"
+ id="path2824" />
+<path
+ style="fill:#000000;stroke-width:0"
+ d="M 391.14,697.93 L 391.14,697.93 L 391.14,697.93 L 391.14,697.93 L 391.14,697.93 L 391.14,697.94 L 391.14,697.94 L 391.14,697.94 L 391.14,697.95 L 391.14,697.95 L 391.14,697.95 L 391.14,697.96 L 391.14,697.96 L 391.14,697.97 L 391.14,697.97 L 391.13,697.98 L 391.13,697.98 L 391.13,697.99 L 391.12,697.99 L 391.12,698 L 391.12,698 L 391.11,698.01 L 391.11,698.01 L 391.11,698.01 L 391.1,698.01 L 391.1,698.02 L 391.1,698.02 L 391.1,698.02 L 391.09,698.02 L 391.09,698.02 L 391.09,698.02 L 391.08,698.03 L 391.08,698.03 L 391.07,698.03 L 391.07,698.03 L 391.07,698.03 L 391.06,698.03 L 391.06,698.03 L 391.05,698.04 L 391.05,698.04 L 391.04,698.04 L 391.04,698.04 L 391.03,698.04 L 391.03,698.04 L 391.02,698.04 L 391.01,698.04 C 390.79,698.04 390.06,697.96 389.8,697.94 C 389.72,697.93 389.61,697.92 389.61,697.74 C 389.61,697.62 389.7,697.62 389.85,697.62 C 390.33,697.62 390.35,697.55 390.35,697.45 C 390.35,697.38 390.26,697.04 390.21,696.83 L 389.39,693.59 C 389.27,693.09 389.23,692.93 389.23,692.58 C 389.23,691.63 389.76,691.02 390.5,691.02 L 390.5,691.23 C 390.16,691.23 389.83,691.5 389.83,692.24 C 389.83,692.43 389.83,692.62 389.99,693.25 L 390.21,694.16 C 390.27,694.38 390.27,694.4 390.36,694.51 C 390.85,695.16 391.29,695.31 391.55,695.31 C 391.91,695.31 392.18,695.01 392.18,694.37 C 392.18,693.78 391.85,692.64 391.67,692.26 C 391.34,691.59 390.89,691.23 390.5,691.23 L 390.5,691.02 C 391.67,691.02 392.9,692.5 392.9,693.93 C 392.9,694.84 392.37,695.53 391.57,695.53 C 391.11,695.53 390.7,695.24 390.41,694.93 L 391.14,697.93 z"
+ id="path2826" />
+<path
+ style="fill:#000000;stroke-width:0"
+ d="M 398.1,697.49 L 399.44,697.49 L 399.44,697.96 C 399,697.93 397.94,697.93 397.45,697.93 C 396.96,697.93 395.88,697.93 395.45,697.96 L 395.45,697.49 L 396.79,697.49 L 396.79,693.07 C 395.64,693.41 395.61,694.64 395.61,695.27 C 395.6,696.16 395.32,696.58 394.72,696.58 L 394,696.58 C 393.85,696.58 393.68,696.58 393.68,696.4 C 393.68,696.25 393.8,696.23 393.91,696.22 C 394.29,696.15 394.3,695.39 394.3,695.34 C 394.3,694.99 394.31,694.1 394.9,693.47 C 395.4,692.93 396.08,692.72 396.79,692.65 L 396.79,691.59 L 395.45,691.59 L 395.45,691.12 C 395.88,691.16 396.95,691.16 397.44,691.16 C 397.93,691.16 399,691.16 399.44,691.12 L 399.44,691.59 L 398.1,691.59 L 398.1,692.65 C 399.02,692.73 399.61,693.04 399.96,693.36 C 400.65,694 400.69,694.95 400.69,695.08 C 400.69,695.53 400.7,696.15 401.11,696.22 C 401.17,696.23 401.3,696.25 401.3,696.4 C 401.3,696.58 401.14,696.58 400.98,696.58 L 400.27,696.58 C 399.93,696.58 399.39,696.53 399.38,695.16 C 399.37,693.95 398.94,693.29 398.1,693.06 L 398.1,697.49 z"
+ id="path2828" />
+<path
+ style="fill:#000000;stroke-width:0"
+ d="M 407.16,696.81 L 407.17,696.81 L 407.18,696.81 L 407.19,696.81 L 407.2,696.81 L 407.21,696.81 L 407.22,696.81 L 407.23,696.81 L 407.24,696.81 L 407.25,696.81 L 407.26,696.82 L 407.27,696.82 L 407.29,696.82 L 407.3,696.82 L 407.31,696.82 L 407.32,696.83 L 407.33,696.83 L 407.34,696.84 L 407.35,696.84 L 407.36,696.85 L 407.36,696.85 L 407.37,696.86 L 407.38,696.87 L 407.39,696.87 L 407.39,696.88 L 407.39,696.88 L 407.4,696.89 L 407.4,696.89 L 407.4,696.9 L 407.41,696.9 L 407.41,696.91 L 407.41,696.91 L 407.41,696.92 L 407.41,696.92 L 407.42,696.93 L 407.42,696.94 L 407.42,696.94 L 407.42,696.95 L 407.42,696.96 L 407.42,696.96 L 407.42,696.97 L 407.42,696.98 C 407.42,697.15 407.26,697.15 407.16,697.15 L 402.97,697.15 C 402.87,697.15 402.71,697.15 402.71,696.98 C 402.71,696.81 402.88,696.81 402.97,696.81 L 407.16,696.81 z"
+ id="path2830" />
+</g> <g
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
+ ns0:text="\\begin{align*}\n&amp;\\sqrt{T_{\\uparrow\\uparrow}}\\mathbf{\\Psi^\\uparrow}\\\\\n+&amp;\\sqrt{T_{\\downarrow\\uparrow}}\\mathbf{\\Psi^\\downarrow}\n\\end{align*}"
+ text-anchor="start"
+ word-spacing="normal"
+ letter-spacing="normal"
+ font-size-adjust="none"
+ font-stretch="normal"
+ font-weight="normal"
+ font-variant="normal"
+ font-style="normal"
+ fill-opacity="1"
+ fill-rule="even-odd"
+ fill="none"
+ stroke-opacity="1"
+ stroke-dashoffset="0"
+ stroke-dasharray="none"
+ stroke-miterlimit="10.433"
+ stroke-linejoin="miter"
+ stroke-linecap="butt"
+ stroke="black"
+ xml:space="preserve"
+ transform="matrix(1.6085256,0,0,-1.6085256,-121.67076,1351.2203)"
+ id="g2956">
+<path
+ id="path2958"
+ fill="black"
+ stroke-width="0"
+ d="M384.41,704.06 L384.43,704.06 L384.44,704.06 L384.46,704.06 L384.47,704.06 L384.48,704.06 L384.49,704.06 L384.51,704.06 L384.52,704.06 L384.53,704.06 L384.54,704.06 L384.55,704.06 L384.56,704.07 L384.58,704.07 L384.6,704.07 L384.61,704.07 L384.63,704.07 L384.64,704.07 L384.66,704.08 L384.67,704.08 L384.68,704.08 L384.69,704.09 L384.7,704.09 L384.71,704.1 L384.72,704.1 L384.73,704.11 L384.74,704.12 L384.75,704.12 L384.75,704.13 L384.76,704.14 L384.77,704.15 L384.78,704.16 L384.78,704.17 L384.79,704.19 L384.8,704.2 L384.81,704.21 L384.82,704.23 L384.82,704.25 L384.83,704.26 L390.28,715.64 C390.35,715.77,390.35,715.79,390.35,715.82 C390.35,715.93,390.27,716.02,390.15,716.02 C390.02,716.02,389.98,715.93,389.93,715.82 L384.79,705.1 L382.67,710.04 L381.29,708.97 L381.43,708.82 L382.14,709.35 Z " />
+<line
+ id="line2960"
+ stroke-width="0.398"
+ y2="715.82"
+ x2="404.64"
+ y1="715.82"
+ x1="390.16" />
+<path
+ id="path2962"
+ fill="black"
+ stroke-width="0"
+ d="M394.41,713.17 L394.42,713.2 L394.42,713.22 L394.43,713.24 L394.44,713.26 L394.44,713.29 L394.45,713.31 L394.45,713.32 L394.46,713.34 L394.47,713.36 L394.47,713.37 L394.48,713.39 L394.48,713.4 L394.49,713.41 L394.5,713.43 L394.5,713.44 L394.51,713.45 L394.51,713.46 L394.52,713.47 L394.53,713.47 L394.53,713.48 L394.54,713.49 L394.55,713.5 L394.56,713.5 L394.56,713.51 L394.57,713.51 L394.58,713.52 L394.59,713.52 L394.6,713.53 L394.61,713.53 L394.62,713.53 L394.63,713.54 L394.64,713.54 C394.73,713.56,395.06,713.56,395.27,713.56 C396.27,713.56,396.72,713.52,396.72,712.74 C396.72,712.59,396.68,712.2,396.64,711.94 C396.63,711.91,396.61,711.78,396.61,711.76 C396.61,711.7,396.64,711.63,396.73,711.63 C396.84,711.63,396.86,711.71,396.88,711.85 L397.15,713.59 C397.16,713.63,397.17,713.73,397.17,713.76 C397.17,713.87,397.07,713.87,396.9,713.87 H391.37 C391.13,713.87,391.12,713.86,391.05,713.67 L390.46,711.91 C390.45,711.9,390.4,711.76,390.4,711.73 C390.4,711.67,390.45,711.63,390.52,711.63 C390.62,711.63,390.63,711.67,390.69,711.84 C391.22,713.38,391.48,713.56,392.96,713.56 H393.35 C393.62,713.56,393.62,713.52,393.62,713.44 C393.62,713.38,393.6,713.26,393.58,713.23 L392.25,707.91 C392.16,707.54,392.13,707.43,391.06,707.43 C390.7,707.43,390.65,707.43,390.65,707.24 C390.65,707.12,390.76,707.12,390.82,707.12 C391.08,707.12,391.36,707.14,391.63,707.14 C391.91,707.14,392.2,707.15,392.48,707.15 C392.76,707.15,393.04,707.14,393.31,707.14 C393.6,707.14,393.89,707.12,394.17,707.12 C394.27,707.12,394.39,707.12,394.39,707.32 C394.39,707.43,394.31,707.43,394.05,707.43 C393.8,707.43,393.67,707.43,393.42,707.45 C393.13,707.48,393.05,707.51,393.05,707.67 C393.05,707.68,393.05,707.73,393.09,707.88 Z " />
+<path
+ id="path2964"
+ fill="black"
+ stroke-width="0"
+ d="M398.19,709.84 L398.23,709.79 L398.27,709.74 L398.31,709.7 L398.36,709.65 L398.4,709.61 L398.45,709.57 L398.49,709.53 L398.54,709.5 L398.58,709.46 L398.63,709.43 L398.67,709.4 L398.71,709.37 L398.76,709.34 L398.8,709.31 L398.84,709.29 L398.88,709.27 L398.92,709.24 L398.96,709.22 L399,709.2 L399.04,709.19 L399.07,709.17 L399.1,709.16 L399.14,709.14 L399.16,709.13 L399.19,709.12 L399.21,709.11 L399.24,709.11 L399.26,709.1 L399.27,709.09 L399.29,709.09 L399.3,709.09 L399.3,709.09 C399.37,709.09,399.4,709.15,399.4,709.21 C399.4,709.3,399.38,709.31,399.26,709.36 C398.7,709.58,398.36,709.93,398.12,710.39 C398.1,710.43,398.08,710.47,398.02,710.47 C397.99,710.47,397.97,710.46,397.95,710.44 C397.94,710.43,397.94,710.43,397.87,710.3 C397.69,709.98,397.36,709.6,396.76,709.35 C396.65,709.31,396.63,709.3,396.63,709.21 C396.63,709.15,396.65,709.09,396.73,709.09 C396.79,709.09,397.41,709.31,397.85,709.84 V704.53 C397.85,704.44,397.85,704.28,398.01,704.28 C398.19,704.28,398.19,704.43,398.19,704.53 Z " />
+<path
+ id="path2966"
+ fill="black"
+ stroke-width="0"
+ d="M402.27,709.84 L402.31,709.79 L402.35,709.74 L402.39,709.7 L402.44,709.65 L402.48,709.61 L402.53,709.57 L402.57,709.53 L402.62,709.5 L402.66,709.46 L402.71,709.43 L402.75,709.4 L402.79,709.37 L402.84,709.34 L402.88,709.31 L402.92,709.29 L402.96,709.27 L403,709.24 L403.04,709.22 L403.08,709.2 L403.12,709.19 L403.15,709.17 L403.18,709.16 L403.22,709.14 L403.24,709.13 L403.27,709.12 L403.29,709.11 L403.32,709.11 L403.34,709.1 L403.35,709.09 L403.37,709.09 L403.38,709.09 L403.38,709.09 C403.45,709.09,403.48,709.15,403.48,709.21 C403.48,709.3,403.46,709.31,403.33,709.36 C402.78,709.58,402.44,709.93,402.2,710.39 C402.18,710.43,402.16,710.47,402.1,710.47 C402.07,710.47,402.05,710.46,402.03,710.44 C402.02,710.43,402.02,710.43,401.95,710.3 C401.77,709.98,401.45,709.6,400.84,709.35 C400.73,709.31,400.71,709.3,400.71,709.21 C400.71,709.15,400.73,709.09,400.81,709.09 C400.87,709.09,401.49,709.31,401.93,709.84 V704.53 C401.93,704.44,401.93,704.28,402.09,704.28 C402.27,704.28,402.27,704.43,402.27,704.53 Z " />
+<path
+ id="path2968"
+ fill="black"
+ stroke-width="0"
+ d="M409.69,713.49 H411.04 V713.96 C410.6,713.93,409.53,713.93,409.04,713.93 C408.55,713.93,407.48,713.93,407.04,713.96 V713.49 H408.39 V709.07 C407.24,709.4,407.2,710.64,407.2,711.27 C407.19,712.15,406.91,712.57,406.31,712.57 H405.6 C405.45,712.57,405.28,712.57,405.28,712.39 C405.28,712.24,405.4,712.22,405.51,712.21 C405.89,712.14,405.89,711.39,405.89,711.34 C405.89,710.99,405.9,710.1,406.49,709.46 C406.99,708.93,407.68,708.72,408.39,708.65 V707.59 H407.04 V707.12 C407.48,707.15,408.55,707.15,409.03,707.15 C409.52,707.15,410.6,707.15,411.04,707.12 V707.59 H409.69 V708.65 C410.62,708.73,411.2,709.03,411.55,709.35 C412.24,710,412.28,710.95,412.28,711.08 C412.28,711.53,412.29,712.14,412.7,712.21 C412.77,712.22,412.9,712.24,412.9,712.39 C412.9,712.57,412.73,712.57,412.58,712.57 H411.86 C411.52,712.57,410.99,712.53,410.98,711.16 C410.97,709.95,410.54,709.28,409.69,709.05 Z " />
+<path
+ id="path2970"
+ fill="black"
+ stroke-width="0"
+ d="M415.76,715.45 L415.8,715.4 L415.84,715.35 L415.89,715.31 L415.93,715.26 L415.97,715.22 L416.02,715.18 L416.06,715.14 L416.11,715.11 L416.15,715.07 L416.2,715.04 L416.24,715.01 L416.29,714.98 L416.33,714.95 L416.37,714.92 L416.42,714.9 L416.46,714.88 L416.5,714.85 L416.54,714.83 L416.57,714.81 L416.61,714.8 L416.64,714.78 L416.68,714.77 L416.71,714.75 L416.74,714.74 L416.76,714.73 L416.79,714.72 L416.81,714.72 L416.83,714.71 L416.85,714.7 L416.86,714.7 L416.87,714.7 L416.88,714.7 C416.95,714.7,416.97,714.76,416.97,714.82 C416.97,714.91,416.95,714.92,416.83,714.97 C416.28,715.19,415.93,715.54,415.69,716 C415.67,716.04,415.65,716.08,415.59,716.08 C415.56,716.08,415.55,716.07,415.52,716.05 C415.52,716.04,415.52,716.04,415.44,715.91 C415.27,715.59,414.94,715.21,414.33,714.96 C414.23,714.92,414.21,714.91,414.21,714.82 C414.21,714.76,414.23,714.7,414.3,714.7 C414.37,714.7,414.99,714.92,415.42,715.45 V710.15 C415.42,710.05,415.42,709.89,415.59,709.89 C415.76,709.89,415.76,710.04,415.76,710.15 Z " />
+<path
+ id="path2972"
+ fill="black"
+ stroke-width="0"
+ d="M376.52,692.55 H379.3 C379.44,692.55,379.63,692.55,379.63,692.75 C379.63,692.95,379.44,692.95,379.3,692.95 H376.52 V695.74 C376.52,695.88,376.52,696.07,376.32,696.07 C376.12,696.07,376.12,695.88,376.12,695.74 V692.95 H373.33 C373.19,692.95,373,692.95,373,692.75 C373,692.55,373.19,692.55,373.33,692.55 H376.12 V689.76 C376.12,689.62,376.12,689.44,376.32,689.44 C376.52,689.44,376.52,689.62,376.52,689.76 Z " />
+<path
+ id="path2974"
+ fill="black"
+ stroke-width="0"
+ d="M384.41,687.2 L384.43,687.2 L384.44,687.2 L384.46,687.2 L384.47,687.2 L384.48,687.2 L384.49,687.2 L384.51,687.2 L384.52,687.2 L384.53,687.2 L384.54,687.2 L384.55,687.2 L384.56,687.21 L384.58,687.21 L384.6,687.21 L384.61,687.21 L384.63,687.21 L384.64,687.21 L384.66,687.22 L384.67,687.22 L384.68,687.22 L384.69,687.23 L384.7,687.23 L384.71,687.24 L384.72,687.24 L384.73,687.25 L384.74,687.26 L384.75,687.26 L384.75,687.27 L384.76,687.28 L384.77,687.29 L384.78,687.3 L384.78,687.31 L384.79,687.33 L384.8,687.34 L384.81,687.35 L384.82,687.37 L384.82,687.39 L384.83,687.4 L390.28,698.78 C390.35,698.91,390.35,698.93,390.35,698.96 C390.35,699.07,390.27,699.16,390.15,699.16 C390.02,699.16,389.98,699.07,389.93,698.96 L384.79,688.24 L382.67,693.18 L381.29,692.11 L381.43,691.96 L382.14,692.49 Z " />
+<line
+ id="line2976"
+ stroke-width="0.398"
+ y2="698.96"
+ x2="404.64"
+ y1="698.96"
+ x1="390.16" />
+<path
+ id="path2978"
+ fill="black"
+ stroke-width="0"
+ d="M394.41,696.31 L394.42,696.34 L394.42,696.36 L394.43,696.38 L394.44,696.4 L394.44,696.43 L394.45,696.45 L394.45,696.46 L394.46,696.48 L394.47,696.5 L394.47,696.51 L394.48,696.53 L394.48,696.54 L394.49,696.55 L394.5,696.57 L394.5,696.58 L394.51,696.59 L394.51,696.6 L394.52,696.61 L394.53,696.61 L394.53,696.62 L394.54,696.63 L394.55,696.64 L394.56,696.64 L394.56,696.65 L394.57,696.65 L394.58,696.66 L394.59,696.66 L394.6,696.67 L394.61,696.67 L394.62,696.67 L394.63,696.68 L394.64,696.68 C394.73,696.7,395.06,696.7,395.27,696.7 C396.27,696.7,396.72,696.66,396.72,695.88 C396.72,695.73,396.68,695.34,396.64,695.08 C396.63,695.04,396.61,694.92,396.61,694.9 C396.61,694.84,396.64,694.77,396.73,694.77 C396.84,694.77,396.86,694.84,396.88,694.99 L397.15,696.73 C397.16,696.77,397.17,696.87,397.17,696.9 C397.17,697.01,397.07,697.01,396.9,697.01 H391.37 C391.13,697.01,391.12,697,391.05,696.81 L390.46,695.05 C390.45,695.03,390.4,694.9,390.4,694.88 C390.4,694.82,390.45,694.77,390.52,694.77 C390.62,694.77,390.63,694.82,390.69,694.97 C391.22,696.52,391.48,696.7,392.96,696.7 H393.35 C393.62,696.7,393.62,696.66,393.62,696.58 C393.62,696.52,393.6,696.4,393.58,696.37 L392.25,691.05 C392.16,690.68,392.13,690.57,391.06,690.57 C390.7,690.57,390.65,690.57,390.65,690.38 C390.65,690.26,390.76,690.26,390.82,690.26 C391.08,690.26,391.36,690.28,391.63,690.28 C391.91,690.28,392.2,690.29,392.48,690.29 C392.76,690.29,393.04,690.28,393.31,690.28 C393.6,690.28,393.89,690.26,394.17,690.26 C394.27,690.26,394.39,690.26,394.39,690.46 C394.39,690.57,394.31,690.57,394.05,690.57 C393.8,690.57,393.67,690.57,393.42,690.59 C393.13,690.62,393.05,690.65,393.05,690.81 C393.05,690.82,393.05,690.87,393.09,691.02 Z " />
+<path
+ id="path2980"
+ fill="black"
+ stroke-width="0"
+ d="M398.19,693.35 L398.19,693.36 L398.19,693.37 L398.19,693.38 L398.19,693.39 L398.19,693.4 L398.19,693.41 L398.19,693.42 L398.19,693.43 L398.18,693.44 L398.18,693.45 L398.18,693.47 L398.18,693.48 L398.18,693.49 L398.17,693.5 L398.17,693.51 L398.17,693.52 L398.16,693.53 L398.16,693.54 L398.15,693.55 L398.15,693.55 L398.14,693.56 L398.13,693.57 L398.13,693.58 L398.12,693.58 L398.12,693.58 L398.11,693.59 L398.11,693.59 L398.1,693.59 L398.1,693.59 L398.09,693.6 L398.09,693.6 L398.08,693.6 L398.08,693.6 L398.07,693.6 L398.06,693.61 L398.06,693.61 L398.05,693.61 L398.04,693.61 L398.04,693.61 L398.03,693.61 L398.02,693.61 C397.85,693.61,397.85,693.46,397.85,693.35 V688.05 C397.41,688.58,396.79,688.8,396.73,688.8 C396.66,688.8,396.63,688.73,396.63,688.68 C396.63,688.58,396.65,688.58,396.78,688.53 C397.29,688.32,397.65,687.98,397.89,687.55 C397.95,687.44,397.96,687.42,398.02,687.42 C398.08,687.42,398.1,687.45,398.15,687.54 C398.48,688.18,399,688.42,399.28,688.53 C399.38,688.58,399.4,688.58,399.4,688.68 C399.4,688.73,399.38,688.8,399.3,688.8 C399.24,688.8,398.62,688.58,398.19,688.05 Z " />
+<path
+ id="path2982"
+ fill="black"
+ stroke-width="0"
+ d="M402.27,692.97 L402.31,692.93 L402.35,692.88 L402.39,692.84 L402.44,692.79 L402.48,692.75 L402.53,692.71 L402.57,692.67 L402.62,692.64 L402.66,692.6 L402.71,692.57 L402.75,692.54 L402.79,692.51 L402.84,692.48 L402.88,692.45 L402.92,692.43 L402.96,692.41 L403,692.38 L403.04,692.36 L403.08,692.34 L403.12,692.33 L403.15,692.31 L403.18,692.3 L403.22,692.28 L403.24,692.27 L403.27,692.26 L403.29,692.25 L403.32,692.25 L403.34,692.24 L403.35,692.23 L403.37,692.23 L403.38,692.23 L403.38,692.23 C403.45,692.23,403.48,692.29,403.48,692.35 C403.48,692.45,403.46,692.45,403.33,692.5 C402.78,692.72,402.44,693.07,402.2,693.53 C402.18,693.57,402.16,693.61,402.1,693.61 C402.07,693.61,402.05,693.6,402.03,693.58 C402.02,693.58,402.02,693.57,401.95,693.44 C401.77,693.12,401.45,692.74,400.84,692.49 C400.73,692.45,400.71,692.45,400.71,692.35 C400.71,692.29,400.73,692.23,400.81,692.23 C400.87,692.23,401.49,692.45,401.93,692.97 V687.67 C401.93,687.58,401.93,687.42,402.09,687.42 C402.27,687.42,402.27,687.57,402.27,687.67 Z " />
+<path
+ id="path2984"
+ fill="black"
+ stroke-width="0"
+ d="M409.69,696.63 H411.04 V697.1 C410.6,697.07,409.53,697.07,409.04,697.07 C408.55,697.07,407.48,697.07,407.04,697.1 V696.63 H408.39 V692.21 C407.24,692.54,407.2,693.78,407.2,694.41 C407.19,695.29,406.91,695.71,406.31,695.71 H405.6 C405.45,695.71,405.28,695.71,405.28,695.53 C405.28,695.38,405.4,695.36,405.51,695.35 C405.89,695.28,405.89,694.53,405.89,694.48 C405.89,694.13,405.9,693.24,406.49,692.6 C406.99,692.07,407.68,691.86,408.39,691.79 V690.73 H407.04 V690.26 C407.48,690.29,408.55,690.29,409.03,690.29 C409.52,690.29,410.6,690.29,411.04,690.26 V690.73 H409.69 V691.79 C410.62,691.87,411.2,692.17,411.55,692.49 C412.24,693.14,412.28,694.09,412.28,694.22 C412.28,694.67,412.29,695.28,412.7,695.35 C412.77,695.36,412.9,695.38,412.9,695.53 C412.9,695.71,412.73,695.71,412.58,695.71 H411.86 C411.52,695.71,410.99,695.67,410.98,694.3 C410.97,693.09,410.54,692.42,409.69,692.2 Z " />
+<path
+ id="path2986"
+ fill="black"
+ stroke-width="0"
+ d="M415.76,698.96 L415.76,698.97 L415.76,698.98 L415.76,698.99 L415.76,699 L415.76,699.01 L415.76,699.02 L415.76,699.03 L415.76,699.04 L415.76,699.05 L415.76,699.06 L415.75,699.08 L415.75,699.09 L415.75,699.1 L415.75,699.11 L415.74,699.12 L415.74,699.13 L415.74,699.14 L415.73,699.15 L415.73,699.16 L415.72,699.16 L415.71,699.17 L415.71,699.18 L415.7,699.19 L415.69,699.19 L415.69,699.19 L415.69,699.2 L415.68,699.2 L415.68,699.2 L415.67,699.2 L415.67,699.21 L415.66,699.21 L415.65,699.21 L415.65,699.21 L415.64,699.21 L415.64,699.22 L415.63,699.22 L415.62,699.22 L415.62,699.22 L415.61,699.22 L415.6,699.22 L415.59,699.22 C415.42,699.22,415.42,699.07,415.42,698.96 V693.66 C414.99,694.18,414.37,694.41,414.3,694.41 C414.23,694.41,414.21,694.34,414.21,694.29 C414.21,694.19,414.23,694.18,414.35,694.14 C414.86,693.93,415.22,693.59,415.46,693.16 C415.52,693.05,415.53,693.03,415.59,693.03 C415.65,693.03,415.67,693.06,415.72,693.15 C416.05,693.79,416.57,694.03,416.85,694.14 C416.95,694.18,416.97,694.19,416.97,694.29 C416.97,694.34,416.95,694.41,416.88,694.41 C416.81,694.41,416.19,694.18,415.76,693.66 Z " />
</g> </g>
<text
xml:space="preserve"
View
BIN tex/beamsplitter2.jpg
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
View
16 tex/bib.bib
@@ -164,6 +164,22 @@ @article{datta-das
doi = {10.1063/1.102730}
}
+@Article{ishe-ew,
+ title = {Charge Hall effect driven by spin-dependent chemical potential gradients and Onsager relations in mesoscopic systems},
+ author = {Hankiewicz, E. M. and Li, Jian and Jungwirth, Tomas and Niu, Qian and Shen, Shun-Qing and Sinova, Jairo },
+ journal = {Phys. Rev. B},
+ volume = {72},
+ number = {15},
+ pages = {155305},
+ numpages = {5},
+ year = {2005},
+ month = {Oct},
+ doi = {10.1103/PhysRevB.72.155305},
+ publisher = {American Physical Society}
+}
+
+
+
@article{ISHE,
author = {E. Saitoh and M. Ueda and H. Miyajima and G. Tatara},
collaboration = {},
View
BIN tex/comparison-over-phi.pdf
Binary file not shown.
View
6 tex/intro.tex
@@ -42,7 +42,7 @@ \chapter{Introduction}
However, building ferromagnetic contacts or devices on
the nano scale is a serious technological challenge, and combining millions of
-ferromagnetic structures on a single seems hardly possible.
+ferromagnetic structures on a single device seems hardly possible.
In this Diploma Thesis, we therefore investigate how a spin polarized electron
beam can be achieved by using only non-magnetic materials. The Rashba
@@ -64,15 +64,15 @@ \chapter{Introduction}
experimentally accessible in quantum wells at heterojunctions in GaAs,
HgTe and other semiconductors.
-In chapter \ref{sec:theory} we present the basic theoretical underpinning for
+In Chapter \ref{sec:theory} we present the basic theoretical underpinning for
the calculations to come: the Landauer Formula which relates conductance to
the transmission matrix $T$, the Fisher-Lee relation which allows calculation
of $T$ based on the Green's function in sample and lead, the Rashba-Bychkov
spin-orbit coupling which causes all the interesting effects discussed in this
thesis, and finally we present a tight binding model which allows numerical
calculation of the Green's functions and thus $T$.
-In chapter \ref{sec:analytical} we present an analytical model of an electron
+In Chapter \ref{sec:analytical} we present an analytical model of an electron
wave traveling from a normal region to a region with spin-orbit coupling. The
wave is decomposed into two parts of opposite chirality, and we
analyze the transmission and reflection coefficients resolved by chirality.
View
16 tex/khodas.tex
@@ -222,7 +222,7 @@ \section{Interface Between Normal and Spin-Orbit Coupling Regions}
it follows that
\begin{align}
- \phi_c &= -\sin ^{-1}\left(a-\sqrt{a^2+1}\right)
+ \phi_c &= -\sin ^{-1}\left(\ta-\sqrt{\ta^2+1}\right)
\end{align}
Figure \ref{fig:critical-angle} shows the critical angle as a function
@@ -307,14 +307,22 @@ \section{Generalization to two Spin-Orbit Regions}
\ref{fig:plots-nonzero}, and in the region $\phi < \phi+_{B,c}$ the various transmission and reflection
coefficients look very similar to the case with $\ta_A = 0$.
-The second gray line is critical angle $\phi^+_{c2}$ associated with
+The second gray line is the critical angle $\phi^+_{c2}$ associated with
$\ta_A$. For
$\phi > \phi^+_{A,c}$ the momentum in $x$ direction $p_{x,A}$ is again
imaginary, just like if we had another interface to a normal region
left of the $A$ region.
-It follows the same $\ta$ dependency, namely $\phi^+_{c2} =
--\sin^{-1}(\ta_A - \sqrt{1+\ta_A^2})$.
+$p_{x,A}$ has the same structural dependence on $\ta_A$ as $p_{x,B}$
+has on $\ta_B$:
+
+\begin{align}
+ p_{x,A}^+ = \sqrt{ p_A^2 - p_z^2} = p \sqrt{(\sqrt{1+\ta_A^2} -
+ \ta_A)^2 - \sin^2 \phi^+}
+\end{align}
+
+It follows that $\phi^+_{c2}$ has a similar form as $\phi^+_{c1}$,
+namely $\phi^+_{c2} = -\sin^{-1}(\ta_A - \sqrt{1+\ta_A^2})$.
%
%\begin{figure}
View
23 tex/numerics.tex
@@ -287,7 +287,14 @@ \subsection{Comparison to Analytical Results}
\begin{center}
\includegraphics[width=0.8\textwidth]{adapting-pic.pdf}
\end{center}
- \caption{Injecting one spin-up charge carrier into the system}
+ \caption{Injecting one spin-up charge carrier into the system notionally
+ splits up the wave into two wave functions with $+$ and $-$ chirality.
+ At the interface a part of the wave is scattered, and
+ $\mathbf{\psi^\pm}$
+ describe the injected and reflected wave functions left of the
+ interface. The transmitted fraction of the wave function is then
+ projected onto the $\uparrow,\downarrow$ bases when it reaches the right
+ lead.}
\end{figure}
% Since there is no dissipation in our model, and we assume that the mere
@@ -438,7 +445,7 @@ \subsection{Comparison to Analytical Results}
(figure \ref{fig:n-so-rel}).
To understand better why we don't get a very clear picture of the critical
-angle the numerical results, we look at \ref{eq:a-n-left} and for a moment
+angle, we look at \ref{eq:a-n-left} and for a moment
ignore the global phases that the $\exp$ functions provide, and obtain a
simplified expression for $a$ and $b$.
@@ -457,7 +464,7 @@ \subsection{Comparison to Analytical Results}
T_{2\uparrow,1\uparrow} &\approx \left|a \chi_{SO}^{+U} t_{++}
+ b \chi_{SO}^{-U} t_{--} \right|^2\nonumber\\
T_{2\downarrow,1\downarrow} &\approx \left|c \chi_{SO}^{-D} t_{--}
- + d \chi_{SO}^{+D} t_{--} \right|^2
+ + d \chi_{SO}^{+D} t_{++} \right|^2
\label{eq:simplfied-t}
\end{align}
@@ -533,19 +540,21 @@ \section{Relation to experiments}
\begin{center}
\includegraphics[width=0.7\textwidth]{beamsplitter2.jpg}
\end{center}
- \caption{Experimental realization of a beam splitter, with two
+ \caption{Experimental realization of a beam splitter in a HgTe/CdTe quantum
+ well, with two
collimating quantum point contact on top and bottom. In the middle
there is a strip at angle $\phi = 45^\circ$ where an electric field
can be applied by a gate. Image courtesy of M. Mühlbauer,
- Physikalisches Institut, Universität Würzburg}
+ Physikalisches Institut, Universität Würzburg\cite{mathias}}
\label{fig:experiment}
\end{figure}
It is possible to realize interfaces between two spin-orbit coupling regimes
in experiments. Figure \ref{fig:experiment} shows such a sample as produced
by the group of H. Buhmann in our department \cite{mathias}.
-It has two wide contacts on the left and right side, and two collimating point
+It consists of a two-dimensional electron gas in a HgTe/CdTe quantum well. It has
+two wide leads on the left and right side, and two collimating point quantum
contacts on the top and bottom. At an angle of $45^{\circ}$ there is a stripe
across the sample. Inside the strip the electric field, and thus the strength
of the spin-orbit coupling strength can be tuned by a gate electrode that is
@@ -558,7 +567,7 @@ \section{Relation to experiments}
scatters electrons too.
The spin polarization can be measured via the Inverse Spin-Hall Effect
-\cite{ISHE} as an electrical current.
+\cite{ishe-ew,ISHE} as an electrical current.
%For $\phi > \phi_c$, the wave $\exp{i p_x^+ x}\exp{i p_z z} t_{++}\chi_{SO}^+$
%does not propagate, because $p_x^+$ is imaginary. That means that the relative
View
BIN tex/rashba-dispersion.jpg
Sorry, something went wrong. Reload?
Sorry, we cannot display this file.
Sorry, this file is invalid so it cannot be displayed.
View
BIN tex/setup-simple.pdf
Binary file not shown.
View
452 tex/setup-simple.svg
@@ -35,17 +35,17 @@
showgrid="false"
inkscape:window-width="918"
inkscape:window-height="838"
- inkscape:window-x="70"
- inkscape:window-y="31" />
+ inkscape:window-x="69"
+ inkscape:window-y="12" />
<defs
id="defs4">
<inkscape:perspective
- sodipodi:type="inkscape:persp3d"
- inkscape:vp_x="0 : 526.18109 : 1"
- inkscape:vp_y="0 : 1000 : 0"
- inkscape:vp_z="744.09448 : 526.18109 : 1"
+ id="perspective10"
inkscape:persp3d-origin="372.04724 : 350.78739 : 1"
- id="perspective10" />
+ inkscape:vp_z="744.09448 : 526.18109 : 1"
+ inkscape:vp_y="0 : 1000 : 0"
+ inkscape:vp_x="0 : 526.18109 : 1"
+ sodipodi:type="inkscape:persp3d" />
</defs>
<metadata
id="metadata7">
@@ -59,202 +59,201 @@
</rdf:RDF>
</metadata>
<g
- inkscape:label="Layer 1"
- inkscape:groupmode="layer"
+ transform="translate(-107.58632,-95.505131)"
id="layer1"
- transform="translate(-107.58632,-95.505131)">
+ inkscape:groupmode="layer"
+ inkscape:label="Layer 1">
<g
id="g3523">
<path
- id="path2383"
+ style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0;stroke-opacity:1"
d="M 108.08632,236.6281 L 404.06102,236.6281 L 503.05597,237.63825"
- style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0;stroke-opacity:1" />
+ id="path2383" />
<path
- id="path3155"
+ style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.71534795;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:0.71534797, 0.71534797;stroke-dashoffset:0;stroke-opacity:1"
d="M 305.68225,95.862805 L 305.68225,307.58772 L 304.95964,378.40355"
- style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.71534795;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:0.71534797, 0.71534797;stroke-dashoffset:0;stroke-opacity:1" />
+ id="path3155" />
</g>
<g
- id="g3165"
- transform="matrix(-0.170924,-0.2960491,0.8115767,-0.468564,0.9920758,438.6628)">
+ transform="matrix(-0.170924,-0.2960491,0.8115767,-0.468564,0.9920758,438.6628)"
+ id="g3165">
<path
- transform="matrix(0,1,-1,0,441.73404,314.70284)"
- d="M 74.787321,377.58029 L 53.52007,389.85894 L 53.52007,365.30164 L 74.787321,377.58029 z"
- inkscape:randomized="0"
- inkscape:rounded="0"
- inkscape:flatsided="true"
- sodipodi:arg2="1.0471976"
- sodipodi:arg1="0"
- sodipodi:r2="7.0890832"
- sodipodi:r1="14.178167"
- sodipodi:cy="377.58029"
- sodipodi:cx="60.609154"
- sodipodi:sides="3"
- id="path3161"
+ sodipodi:type="star"
style="stroke-width:1;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0"
- sodipodi:type="star" />
+ id="path3161"
+ sodipodi:sides="3"
+ sodipodi:cx="60.609154"
+ sodipodi:cy="377.58029"
+ sodipodi:r1="14.178167"
+ sodipodi:r2="7.0890832"
+ sodipodi:arg1="0"
+ sodipodi:arg2="1.0471976"
+ inkscape:flatsided="true"
+ inkscape:rounded="0"
+ inkscape:randomized="0"
+ d="M 74.787321,377.58029 L 53.52007,389.85894 L 53.52007,365.30164 L 74.787321,377.58029 z"
+ transform="matrix(0,1,-1,0,441.73404,314.70284)" />
<rect
- y="228.82176"
- x="59.102985"
- height="139.40105"
- width="10.101525"
+ style="stroke-width:1;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0"
id="rect3163"
- style="stroke-width:1;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0" />
+ width="10.101525"
+ height="139.40105"
+ x="59.102985"
+ y="228.82176" />
</g>
<g
id="g3257">
<path
- transform="matrix(0.5389814,-0.5389814,0.1966111,0.1966111,278.37546,115.78642)"
- d="M 74.787321,377.58029 L 53.52007,389.85894 L 53.52007,365.30164 L 74.787321,377.58029 z"
- inkscape:randomized="0"
- inkscape:rounded="0"
- inkscape:flatsided="true"
- sodipodi:arg2="1.0471976"
- sodipodi:arg1="0"
- sodipodi:r2="7.0890832"
- sodipodi:r1="14.178167"
- sodipodi:cy="377.58029"
- sodipodi:cx="60.609154"
- sodipodi:sides="3"
- id="path3177"
+ sodipodi:type="star"
style="fill:#ff0000;fill-opacity:1;stroke:#fd0000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0;stroke-opacity:1"
- sodipodi:type="star" />
+ id="path3177"
+ sodipodi:sides="3"
+ sodipodi:cx="60.609154"
+ sodipodi:cy="377.58029"
+ sodipodi:r1="14.178167"
+ sodipodi:r2="7.0890832"
+ sodipodi:arg1="0"
+ sodipodi:arg2="1.0471976"
+ inkscape:flatsided="true"
+ inkscape:rounded="0"
+ inkscape:randomized="0"
+ d="M 74.787321,377.58029 L 53.52007,389.85894 L 53.52007,365.30164 L 74.787321,377.58029 z"
+ transform="matrix(0.5389814,-0.5389814,0.1966111,0.1966111,278.37546,115.78642)" />
<rect
- transform="matrix(-0.7071068,-0.7071068,0.7071068,-0.7071068,0,0)"
- y="49.506268"
- x="-385.10513"
- height="106.25633"
- width="2.8087299"
+ style="fill:#ff0000;fill-opacity:1;stroke:#fd0000;stroke-width:0.46036881;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
id="rect3179"
- style="fill:#ff0000;fill-opacity:1;stroke:#fd0000;stroke-width:0.46036881;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1" />
+ width="2.8087299"
+ height="106.25633"
+ x="-385.10513"
+ y="49.506268"
+ transform="matrix(-0.7071068,-0.7071068,0.7071068,-0.7071068,0,0)" />
</g>
<g
id="g3261">
<path
- transform="matrix(0.9075525,-0.4344146,0.1584669,0.3310594,323.82863,73.496685)"
- d="M 74.787321,377.58029 L 53.52007,389.85894 L 53.52007,365.30164 L 74.787321,377.58029 z"
- inkscape:randomized="0"
- inkscape:rounded="0"
- inkscape:flatsided="true"
- sodipodi:arg2="1.0471976"
- sodipodi:arg1="0"
- sodipodi:r2="7.0890832"
- sodipodi:r1="14.178167"
- sodipodi:cy="377.58029"
- sodipodi:cx="60.609154"
- sodipodi:sides="3"
- id="path3183"
+ sodipodi:type="star"
style="fill:#0000ff;fill-opacity:1;stroke:#0000ff;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:1, 1;stroke-dashoffset:0;stroke-opacity:1"
- sodipodi:type="star" />
+ id="path3183"
+ sodipodi:sides="3"
+ sodipodi:cx="60.609154"
+ sodipodi:cy="377.58029"
+ sodipodi:r1="14.178167"
+ sodipodi:r2="7.0890832"
+ sodipodi:arg1="0"
+ sodipodi:arg2="1.0471976"
+ inkscape:flatsided="true"
+ inkscape:rounded="0"
+ inkscape:randomized="0"
+ d="M 74.787321,377.58029 L 53.52007,389.85894 L 53.52007,365.30164 L 74.787321,377.58029 z"
+ transform="matrix(0.9075525,-0.4344146,0.1584669,0.3310594,323.82863,73.496685)" />
<rect
- transform="matrix(-0.4317529,-0.9019919,0.9019919,-0.4317529,0,0)"
- y="173.94788"
- x="-346.54501"
- height="140.26042"
- width="3.7075775"
+ style="fill:#0000ff;fill-opacity:1;stroke:#0000ff;stroke-width:0.60799998;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
id="rect3185"
- style="fill:#0000ff;fill-opacity:1;stroke:#0000ff;stroke-width:0.60799998;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1" />
+ width="3.7075775"
+ height="140.26042"
+ x="-346.54501"
+ y="173.94788"
+ transform="matrix(-0.4317529,-0.9019919,0.9019919,-0.4317529,0,0)" />
</g>
<g
- id="g3247"
- transform="matrix(1.573764,0,0,1.573764,-177.46866,-135.94915)">
+ transform="matrix(1.573764,0,0,1.573764,-177.46866,-135.94915)"
+ id="g3247">
<path
- sodipodi:open="true"
- sodipodi:end="3.075953"
- sodipodi:start="2.5604567"
- transform="matrix(0.9989964,4.4790381e-2,-4.4790381e-2,0.9989964,10.907442,-13.471751)"
- d="M 274.83619,257.18225 A 37.375645,37.375645 0 0 1 268.78108,239.11556"
- sodipodi:ry="37.375645"
- sodipodi:rx="37.375645"
- sodipodi:cy="236.664"
- sodipodi:cx="306.07623"
- id="path3209"
+ sodipodi:type="arc"
style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- sodipodi:type="arc" />
+ id="path3209"
+ sodipodi:cx="306.07623"
+ sodipodi:cy="236.664"
+ sodipodi:rx="37.375645"
+ sodipodi:ry="37.375645"
+ d="M 274.83619,257.18225 A 37.375645,37.375645 0 0 1 268.78108,239.11556"
+ transform="matrix(0.9989964,4.4790381e-2,-4.4790381e-2,0.9989964,10.907442,-13.471751)"
+ sodipodi:start="2.5604567"
+ sodipodi:end="3.075953"
+ sodipodi:open="true" />
<path
- transform="matrix(1.8611748,0,0,1.8611748,-209.86294,-217.04048)"
- d="M 259.64285,253.25503 L 258.64319,252.76075 L 259.57108,252.14216 L 259.64285,253.25503 z"
- inkscape:randomized="0"
- inkscape:rounded="0"
- inkscape:flatsided="true"
- sodipodi:arg2="2.0299913"
- sodipodi:arg1="0.98279372"
- sodipodi:r2="0.32192421"
- sodipodi:r1="0.64384842"
- sodipodi:cy="252.71931"
- sodipodi:cx="259.28571"
- sodipodi:sides="3"
- id="path3211"
+ sodipodi:type="star"
style="fill:#000000;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- sodipodi:type="star" />
+ id="path3211"
+ sodipodi:sides="3"
+ sodipodi:cx="259.28571"
+ sodipodi:cy="252.71931"
+ sodipodi:r1="0.64384842"
+ sodipodi:r2="0.32192421"
+ sodipodi:arg1="0.98279372"
+ sodipodi:arg2="2.0299913"
+ inkscape:flatsided="true"
+ inkscape:rounded="0"
+ inkscape:randomized="0"
+ d="M 259.64285,253.25503 L 258.64319,252.76075 L 259.57108,252.14216 L 259.64285,253.25503 z"
+ transform="matrix(1.8611748,0,0,1.8611748,-209.86294,-217.04048)" />
</g>
<g
- id="g2417"
- transform="translate(3.5714286,0)">
+ transform="translate(3.5714286,0)"
+ id="g2417">
<path
- transform="matrix(1.3614003,1.6507505,-2.1713508,1.3350476,428.59065,-588.56222)"
- sodipodi:open="true"
- sodipodi:end="5.4279125"
- sodipodi:start="4.6800022"
- d="M 305.76937,217.01571 A 20.357143,20.357143 0 0 1 319.7831,221.99763"
- sodipodi:ry="20.357143"
- sodipodi:rx="20.357143"
- sodipodi:cy="237.36218"
- sodipodi:cx="306.42856"
- id="path3225"
+ sodipodi:type="arc"
style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- sodipodi:type="arc" />
+ id="path3225"
+ sodipodi:cx="306.42856"
+ sodipodi:cy="237.36218"
+ sodipodi:rx="20.357143"
+ sodipodi:ry="20.357143"
+ d="M 305.76937,217.01571 A 20.357143,20.357143 0 0 1 319.7831,221.99763"
+ sodipodi:start="4.6800022"
+ sodipodi:end="5.4279125"
+ sodipodi:open="true"
+ transform="matrix(1.3614003,1.6507505,-2.1713508,1.3350476,428.59065,-588.56222)" />
<path
- inkscape:transform-center-y="-3.6959844"
- transform="matrix(2.3192857,-3.9513662,3.9513662,2.3192857,-1226.2631,644.09113)"
- d="M 259.64285,253.25503 L 258.64319,252.76075 L 259.57108,252.14216 L 259.64285,253.25503 z"
- inkscape:randomized="0"
- inkscape:rounded="0"
- inkscape:flatsided="true"
- sodipodi:arg2="2.0299913"
- sodipodi:arg1="0.98279372"
- sodipodi:r2="0.32192421"
- sodipodi:r1="0.64384842"
- sodipodi:cy="252.71931"
- sodipodi:cx="259.28571"
- sodipodi:sides="3"
- id="path3231"
+ sodipodi:type="star"
style="fill:#000000;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- sodipodi:type="star" />
+ id="path3231"
+ sodipodi:sides="3"
+ sodipodi:cx="259.28571"
+ sodipodi:cy="252.71931"
+ sodipodi:r1="0.64384842"
+ sodipodi:r2="0.32192421"
+ sodipodi:arg1="0.98279372"
+ sodipodi:arg2="2.0299913"
+ inkscape:flatsided="true"
+ inkscape:rounded="0"
+ inkscape:randomized="0"
+ d="M 259.64285,253.25503 L 258.64319,252.76075 L 259.57108,252.14216 L 259.64285,253.25503 z"
+ transform="matrix(2.3192857,-3.9513662,3.9513662,2.3192857,-1226.2631,644.09113)"
+ inkscape:transform-center-y="-3.6959844" />
</g>
<path
- sodipodi:type="arc"
- style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- id="path3235"
- sodipodi:cx="306.07144"
- sodipodi:cy="236.64789"
- sodipodi:rx="24.464285"
- sodipodi:ry="24.464285"
- d="M 305.27926,212.19643 A 24.464285,24.464285 0 0 1 327.24141,224.38683"
- sodipodi:start="4.6800022"
- sodipodi:end="5.758221"
+ transform="matrix(2.2090291,1.5796098,-1.5796098,2.2090291,30.348698,-775.25591)"
sodipodi:open="true"
- transform="matrix(2.2090291,1.5796098,-1.5796098,2.2090291,30.348698,-775.25591)" />
+ sodipodi:end="5.758221"
+ sodipodi:start="4.6800022"
+ d="M 305.27926,212.19643 A 24.464285,24.464285 0 0 1 327.24141,224.38683"
+ sodipodi:ry="24.464285"
+ sodipodi:rx="24.464285"
+ sodipodi:cy="236.64789"
+ sodipodi:cx="306.07144"
+ id="path3235"
+ style="fill:none;fill-opacity:1;stroke:#000000;stroke-width:1;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ sodipodi:type="arc" />
<path
- sodipodi:type="star"
- style="fill:#000000;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- id="path3237"
- sodipodi:sides="3"
- sodipodi:cx="259.28571"
- sodipodi:cy="252.71931"
- sodipodi:r1="0.64384842"
- sodipodi:r2="0.32192421"
- sodipodi:arg1="0.98279372"
- sodipodi:arg2="2.0299913"
- inkscape:flatsided="true"
- inkscape:rounded="0"
- inkscape:randomized="0"
+ transform="matrix(3.411048,3.7298071,-3.7298071,3.411048,430.01136,-1651.9341)"
d="M 259.64285,253.25503 L 258.64319,252.76075 L 259.57108,252.14216 L 259.64285,253.25503 z"
- transform="matrix(3.411048,3.7298071,-3.7298071,3.411048,430.01136,-1651.9341)" />
+ inkscape:randomized="0"
+ inkscape:rounded="0"
+ inkscape:flatsided="true"
+ sodipodi:arg2="2.0299913"
+ sodipodi:arg1="0.98279372"
+ sodipodi:r2="0.32192421"
+ sodipodi:r1="0.64384842"
+ sodipodi:cy="252.71931"
+ sodipodi:cx="259.28571"
+ sodipodi:sides="3"
+ id="path3237"
+ style="fill:#000000;fill-opacity:1;stroke:#000000;stroke-width:0.5;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ sodipodi:type="star" />
<g
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
ns0:preamble=""
- ns0:text="$\\varphi$"
+ ns0:text="$\\theta^+$"
word-spacing="normal"
letter-spacing="normal"
font-size-adjust="none"
@@ -265,16 +264,20 @@
fill-rule="even-odd"
stroke-miterlimit="10.433"
xml:space="preserve"
- transform="matrix(1.5197568,0,0,-1.5197568,-83.14647,1322.9304)"
- id="content">
+ transform="matrix(1.2437811,0,0,-1.2437811,76.875285,1047.321)"
+ id="g3403"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
+<path
+ id="path3405"
+ d="M 227.96,712.1 L 227.96,712.17 L 227.96,712.24 L 227.96,712.31 L 227.96,712.38 L 227.95,712.46 L 227.94,712.54 L 227.93,712.62 L 227.92,712.7 L 227.91,712.78 L 227.89,712.87 L 227.87,712.95 L 227.85,713.04 L 227.83,713.12 L 227.81,713.21 L 227.78,713.29 L 227.75,713.37 L 227.71,713.45 L 227.68,713.53 L 227.64,713.6 L 227.59,713.67 L 227.55,713.74 L 227.5,713.8 L 227.44,713.86 L 227.39,713.92 L 227.32,713.97 L 227.29,713.99 L 227.26,714.01 L 227.22,714.03 L 227.19,714.05 L 227.15,714.07 L 227.11,714.09 L 227.07,714.1 L 227.03,714.11 L 226.99,714.12 L 226.95,714.13 L 226.91,714.14 L 226.86,714.14 L 226.82,714.14 L 226.77,714.15 L 226.76,713.93 C 227.25,713.93 227.31,713.29 227.31,712.72 C 227.31,712.23 227.23,711.72 226.99,710.74 L 224.91,710.74 C 225.08,711.38 225.28,712.17 225.67,712.88 C 225.94,713.37 226.31,713.93 226.76,713.93 L 226.77,714.15 C 225.38,714.15 223.85,711.34 223.85,709.05 C 223.85,708.12 224.14,707.01 225.05,707.01 L 225.05,707.23 C 224.72,707.23 224.51,707.52 224.51,708.45 C 224.51,708.87 224.57,709.44 224.83,710.42 L 226.9,710.42 C 226.79,709.96 226.58,709.11 226.2,708.4 C 225.85,707.72 225.48,707.23 225.05,707.23 L 225.05,707.01 C 226.45,707.01 227.96,709.87 227.96,712.1 z"
+ style="fill:#000000;stroke-width:0" />
<path
- id="path3347"
- d="M 225.13,705.43 L 225.12,705.42 L 225.12,705.42 L 225.12,705.41 L 225.12,705.41 L 225.12,705.4 L 225.12,705.4 L 225.11,705.39 L 225.11,705.38 L 225.11,705.37 L 225.1,705.36 L 225.1,705.35 L 225.1,705.34 L 225.1,705.34 L 225.09,705.33 L 225.09,705.32 L 225.09,705.32 L 225.09,705.31 L 225.09,705.3 L 225.09,705.3 L 225.08,705.29 L 225.08,705.29 L 225.08,705.28 L 225.08,705.28 L 225.08,705.28 L 225.08,705.27 L 225.08,705.26 L 225.08,705.26 L 225.08,705.25 L 225.08,705.24 L 225.08,705.23 L 225.08,705.23 C 225.08,705.01 225.27,704.95 225.37,704.95 C 225.41,704.95 225.63,704.98 225.73,705.21 C 225.76,705.29 225.81,705.62 226.08,707.03 C 226.17,707.02 226.24,707.01 226.41,707.01 C 228.07,707.01 229.6,708.58 229.6,710.15 L 229.32,709.93 C 229.32,708.81 228.04,707.59 226.5,707.59 L 226.5,707.59 C 226.42,707.59 226.4,707.59 226.32,707.6 C 226.2,707.6 226.19,707.61 226.19,707.64 C 226.19,707.66 226.36,708.57 226.39,708.72 C 226.7,709.99 227.48,710.95 228.36,710.95 C 229.05,710.95 229.32,710.41 229.32,709.93 L 229.6,710.15 C 229.6,710.93 229.21,711.53 228.46,711.53 C 227.02,711.53 226.42,709.59 225.82,707.65 C 224.75,707.85 224.19,708.41 224.19,709.12 C 224.19,709.4 224.42,710.5 225.02,711.19 C 225.1,711.28 225.1,711.3 225.1,711.32 C 225.1,711.36 225.08,711.42 224.98,711.42 C 224.7,711.42 223.93,709.97 223.93,709.02 C 223.93,708.08 224.59,707.35 225.65,707.1 L 225.13,705.43 z"
+ id="path3407"
+ d="M 231.61,712.31 L 233.74,712.31 C 233.84,712.31 234,712.31 234,712.48 C 234,712.66 233.84,712.66 233.74,712.66 L 231.61,712.66 L 231.61,714.8 C 231.61,714.89 231.61,715.05 231.44,715.05 C 231.27,715.05 231.27,714.89 231.27,714.8 L 231.27,712.66 L 229.13,712.66 C 229.04,712.66 228.87,712.66 228.87,712.49 C 228.87,712.31 229.03,712.31 229.13,712.31 L 231.27,712.31 L 231.27,710.17 C 231.27,710.08 231.27,709.91 231.44,709.91 C 231.61,709.91 231.61,710.08 231.61,710.17 L 231.61,712.31 z"
style="fill:#000000;stroke-width:0" />
</g> <g
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- id="g3403"
- transform="matrix(1.2437811,0,0,-1.2437811,76.875285,1047.321)"
+ id="g3475"
+ transform="matrix(1.4005602,0,0,-1.4005602,47.302452,1214.2939)"
xml:space="preserve"
stroke-miterlimit="10.433"
fill-rule="even-odd"
@@ -285,79 +288,86 @@
font-size-adjust="none"
letter-spacing="normal"
word-spacing="normal"
- ns0:text="$\\theta^+$"
- ns0:preamble="">
+ ns0:text="$\\theta^-$"
+ ns0:preamble=""
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
<path
style="fill:#000000;stroke-width:0"
d="M 227.96,712.1 L 227.96,712.17 L 227.96,712.24 L 227.96,712.31 L 227.96,712.38 L 227.95,712.46 L 227.94,712.54 L 227.93,712.62 L 227.92,712.7 L 227.91,712.78 L 227.89,712.87 L 227.87,712.95 L 227.85,713.04 L 227.83,713.12 L 227.81,713.21 L 227.78,713.29 L 227.75,713.37 L 227.71,713.45 L 227.68,713.53 L 227.64,713.6 L 227.59,713.67 L 227.55,713.74 L 227.5,713.8 L 227.44,713.86 L 227.39,713.92 L 227.32,713.97 L 227.29,713.99 L 227.26,714.01 L 227.22,714.03 L 227.19,714.05 L 227.15,714.07 L 227.11,714.09 L 227.07,714.1 L 227.03,714.11 L 226.99,714.12 L 226.95,714.13 L 226.91,714.14 L 226.86,714.14 L 226.82,714.14 L 226.77,714.15 L 226.76,713.93 C 227.25,713.93 227.31,713.29 227.31,712.72 C 227.31,712.23 227.23,711.72 226.99,710.74 L 224.91,710.74 C 225.08,711.38 225.28,712.17 225.67,712.88 C 225.94,713.37 226.31,713.93 226.76,713.93 L 226.77,714.15 C 225.38,714.15 223.85,711.34 223.85,709.05 C 223.85,708.12 224.14,707.01 225.05,707.01 L 225.05,707.23 C 224.72,707.23 224.51,707.52 224.51,708.45 C 224.51,708.87 224.57,709.44 224.83,710.42 L 226.9,710.42 C 226.79,709.96 226.58,709.11 226.2,708.4 C 225.85,707.72 225.48,707.23 225.05,707.23 L 225.05,707.01 C 226.45,707.01 227.96,709.87 227.96,712.1 z"
- id="path3405" />
+ id="path3477" />
<path
style="fill:#000000;stroke-width:0"
- d="M 231.61,712.31 L 233.74,712.31 C 233.84,712.31 234,712.31 234,712.48 C 234,712.66 233.84,712.66 233.74,712.66 L 231.61,712.66 L 231.61,714.8 C 231.61,714.89 231.61,715.05 231.44,715.05 C 231.27,715.05 231.27,714.89 231.27,714.8 L 231.27,712.66 L 229.13,712.66 C 229.04,712.66 228.87,712.66 228.87,712.49 C 228.87,712.31 229.03,712.31 229.13,712.31 L 231.27,712.31 L 231.27,710.17 C 231.27,710.08 231.27,709.91 231.44,709.91 C 231.61,709.91 231.61,710.08 231.61,710.17 L 231.61,712.31 z"
- id="path3407" />
-</g> <g
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- ns0:preamble=""
- ns0:text="$\\theta^-$"
- word-spacing="normal"
- letter-spacing="normal"
- font-size-adjust="none"
- font-stretch="normal"
- font-weight="normal"
- font-variant="normal"
- font-style="normal"
- fill-rule="even-odd"
- stroke-miterlimit="10.433"
- xml:space="preserve"
- transform="matrix(1.4005602,0,0,-1.4005602,47.302452,1214.2939)"
- id="g3475">
-<path
- id="path3477"
- d="M 227.96,712.1 L 227.96,712.17 L 227.96,712.24 L 227.96,712.31 L 227.96,712.38 L 227.95,712.46 L 227.94,712.54 L 227.93,712.62 L 227.92,712.7 L 227.91,712.78 L 227.89,712.87 L 227.87,712.95 L 227.85,713.04 L 227.83,713.12 L 227.81,713.21 L 227.78,713.29 L 227.75,713.37 L 227.71,713.45 L 227.68,713.53 L 227.64,713.6 L 227.59,713.67 L 227.55,713.74 L 227.5,713.8 L 227.44,713.86 L 227.39,713.92 L 227.32,713.97 L 227.29,713.99 L 227.26,714.01 L 227.22,714.03 L 227.19,714.05 L 227.15,714.07 L 227.11,714.09 L 227.07,714.1 L 227.03,714.11 L 226.99,714.12 L 226.95,714.13 L 226.91,714.14 L 226.86,714.14 L 226.82,714.14 L 226.77,714.15 L 226.76,713.93 C 227.25,713.93 227.31,713.29 227.31,712.72 C 227.31,712.23 227.23,711.72 226.99,710.74 L 224.91,710.74 C 225.08,711.38 225.28,712.17 225.67,712.88 C 225.94,713.37 226.31,713.93 226.76,713.93 L 226.77,714.15 C 225.38,714.15 223.85,711.34 223.85,709.05 C 223.85,708.12 224.14,707.01 225.05,707.01 L 225.05,707.23 C 224.72,707.23 224.51,707.52 224.51,708.45 C 224.51,708.87 224.57,709.44 224.83,710.42 L 226.9,710.42 C 226.79,709.96 226.58,709.11 226.2,708.4 C 225.85,707.72 225.48,707.23 225.05,707.23 L 225.05,707.01 C 226.45,707.01 227.96,709.87 227.96,712.1 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path3479"
d="M 233.59,712.31 L 233.6,712.31 L 233.61,712.31 L 233.62,712.31 L 233.63,712.31 L 233.64,712.31 L 233.65,712.32 L 233.66,712.32 L 233.67,712.32 L 233.68,712.32 L 233.69,712.32 L 233.7,712.32 L 233.71,712.32 L 233.72,712.33 L 233.73,712.33 L 233.75,712.33 L 233.76,712.33 L 233.76,712.34 L 233.77,712.34 L 233.78,712.35 L 233.79,712.35 L 233.8,712.36 L 233.81,712.37 L 233.82,712.38 L 233.82,712.38 L 233.82,712.38 L 233.83,712.39 L 233.83,712.39 L 233.83,712.4 L 233.83,712.4 L 233.84,712.41 L 233.84,712.41 L 233.84,712.42 L 233.84,712.43 L 233.84,712.43 L 233.85,712.44 L 233.85,712.44 L 233.85,712.45 L 233.85,712.46 L 233.85,712.47 L 233.85,712.47 L 233.85,712.48 C 233.85,712.66 233.69,712.66 233.59,712.66 L 229.39,712.66 C 229.3,712.66 229.14,712.66 229.14,712.48 C 229.14,712.31 229.3,712.31 229.39,712.31 L 233.59,712.31 z"
- style="fill:#000000;stroke-width:0" />
+ id="path3479" />
</g> <text
- xml:space="preserve"
- style="font-size:14px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
- x="491.42856"
+ id="text3513"
y="235.93361"
- id="text3513"><tspan
- sodipodi:role="line"
- id="tspan3515"
+ x="491.42856"
+ style="font-size:14px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ xml:space="preserve"><tspan
+ y="235.93361"
x="491.42856"
- y="235.93361">x</tspan></text>
+ id="tspan3515"
+ sodipodi:role="line">x</tspan></text>
<text
- xml:space="preserve"
- style="font-size:14px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
- x="313.57144"
+ id="text3517"
y="103.79075"
- id="text3517"><tspan
- sodipodi:role="line"
- id="tspan3519"
+ x="313.57144"
+ style="font-size:14px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ xml:space="preserve"><tspan
+ y="103.79075"
x="313.57144"
- y="103.79075">z</tspan></text>
+ id="tspan3519"
+ sodipodi:role="line">z</tspan></text>
<text
- xml:space="preserve"
- style="font-size:40px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
- x="140.44347"
+ id="text2451"
y="144.54877"
- id="text2451"><tspan
- sodipodi:role="line"
- id="tspan2453"
+ x="140.44347"
+ style="font-size:40px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ xml:space="preserve"><tspan
+ y="144.54877"
x="140.44347"
- y="144.54877">N</tspan></text>
+ id="tspan2453"
+ sodipodi:role="line">N</tspan></text>
<text
- xml:space="preserve"
- style="font-size:40px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
- x="424.76825"
+ id="text2455"
y="144.52924"
- id="text2455"><tspan
- sodipodi:role="line"
- id="tspan2457"
+ x="424.76825"
+ style="font-size:40px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ xml:space="preserve"><tspan
+ y="144.52924"
x="424.76825"
- y="144.52924">SO</tspan></text>
- </g>
+ id="tspan2457"
+ sodipodi:role="line">SO</tspan></text>
+ <g
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
+ ns0:text="$\\phi$"
+ text-anchor="start"
+ word-spacing="normal"
+ letter-spacing="normal"
+ font-size-adjust="none"
+ font-stretch="normal"
+ font-weight="normal"
+ font-variant="normal"
+ font-style="normal"
+ fill-opacity="1"
+ fill-rule="even-odd"
+ fill="none"
+ stroke-opacity="1"
+ stroke-dashoffset="0"
+ stroke-dasharray="none"
+ stroke-miterlimit="10.433"
+ stroke-linejoin="miter"
+ stroke-linecap="butt"
+ stroke="black"
+ xml:space="preserve"
+ transform="matrix(1.5197568,0,0,-1.5197568,-83.14647,1322.9304)"
+ id="content">
+<path
+ id="path2456"
+ fill="black"
+ stroke-width="0"
+ d="M227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.81 L227.79,713.81 L227.79,713.81 L227.79,713.82 L227.79,713.82 L227.79,713.83 L227.79,713.83 L227.79,713.84 L227.79,713.84 L227.8,713.85 L227.8,713.85 L227.8,713.86 L227.8,713.87 L227.8,713.88 L227.81,713.89 L227.81,713.89 L227.81,713.9 L227.81,713.9 L227.81,713.91 L227.81,713.91 L227.81,713.92 L227.81,713.92 L227.81,713.93 L227.81,713.93 L227.81,713.93 L227.81,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.94 L227.82,713.94 L227.82,713.94 C227.82,713.95,227.82,714.04,227.7,714.04 C227.6,714.04,227.59,714.01,227.55,713.84 L226.97,711.54 C225.38,711.49,223.92,710.16,223.92,708.81 C223.92,707.86,224.62,707.07,225.83,707 L225.88,707.22 C225.29,707.25,224.57,707.6,224.57,708.6 C224.57,709.79,225.43,711.19,226.91,711.32 L225.88,707.22 L225.83,707 C225.75,706.69,225.68,706.38,225.6,706.07 C225.49,705.6,225.38,705.22,225.38,705.19 C225.38,705.09,225.46,705.08,225.51,705.08 C225.55,705.08,225.57,705.09,225.6,705.12 C225.62,705.14,225.68,705.38,225.71,705.52 C225.84,706.01,225.96,706.51,226.09,707 L226.14,707.22 L227.17,711.32 C227.93,711.28,228.49,710.82,228.49,709.94 C228.49,708.77,227.64,707.34,226.14,707.22 L226.09,707 C227.7,707.05,229.14,708.4,229.14,709.73 C229.14,710.52,228.61,711.44,227.23,711.54 Z " />
+</g> </g>
</svg>
View
BIN tex/setup-two-so-regions.pdf
Binary file not shown.
View
124 tex/setup-two-so-regions.svg
@@ -35,8 +35,8 @@
showgrid="false"
inkscape:window-width="1085"
inkscape:window-height="891"
- inkscape:window-x="64"
- inkscape:window-y="-1" />
+ inkscape:window-x="18"
+ inkscape:window-y="36" />
<defs
id="defs4">
<inkscape:perspective
@@ -240,30 +240,6 @@
id="tspan3519"
sodipodi:role="line">z</tspan></text>
<g
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
- ns0:preamble=""
- ns0:text="$\\varphi_+$"
- word-spacing="normal"
- letter-spacing="normal"
- font-size-adjust="none"
- font-stretch="normal"
- font-weight="normal"
- font-variant="normal"
- font-style="normal"
- fill-rule="even-odd"
- stroke-miterlimit="10.433"
- xml:space="preserve"
- transform="matrix(1.5197568,0,0,-1.5197568,-130.14647,1351.9304)"
- id="content">
-<path
- id="path3584"
- d="M 225.13,705.43 L 225.12,705.42 L 225.12,705.42 L 225.12,705.41 L 225.12,705.41 L 225.12,705.4 L 225.12,705.4 L 225.11,705.39 L 225.11,705.38 L 225.11,705.37 L 225.1,705.36 L 225.1,705.35 L 225.1,705.34 L 225.1,705.34 L 225.09,705.33 L 225.09,705.32 L 225.09,705.32 L 225.09,705.31 L 225.09,705.3 L 225.09,705.3 L 225.08,705.29 L 225.08,705.29 L 225.08,705.28 L 225.08,705.28 L 225.08,705.28 L 225.08,705.27 L 225.08,705.26 L 225.08,705.26 L 225.08,705.25 L 225.08,705.24 L 225.08,705.23 L 225.08,705.23 C 225.08,705.01 225.27,704.95 225.37,704.95 C 225.41,704.95 225.63,704.98 225.73,705.21 C 225.76,705.29 225.81,705.62 226.08,707.03 C 226.17,707.02 226.24,707.01 226.41,707.01 C 228.07,707.01 229.6,708.58 229.6,710.15 L 229.32,709.93 C 229.32,708.81 228.04,707.59 226.5,707.59 L 226.5,707.59 C 226.42,707.59 226.4,707.59 226.32,707.6 C 226.2,707.6 226.19,707.61 226.19,707.64 C 226.19,707.66 226.36,708.57 226.39,708.72 C 226.7,709.99 227.48,710.95 228.36,710.95 C 229.05,710.95 229.32,710.41 229.32,709.93 L 229.6,710.15 C 229.6,710.93 229.21,711.53 228.46,711.53 C 227.02,711.53 226.42,709.59 225.82,707.65 C 224.75,707.85 224.19,708.41 224.19,709.12 C 224.19,709.4 224.42,710.5 225.02,711.19 C 225.1,711.28 225.1,711.3 225.1,711.32 C 225.1,711.36 225.08,711.42 224.98,711.42 C 224.7,711.42 223.93,709.97 223.93,709.02 C 223.93,708.08 224.59,707.35 225.65,707.1 L 225.13,705.43 z"
- style="fill:#000000;stroke-width:0" />
-<path
- id="path3586"
- d="M 233.18,707.21 L 235.31,707.21 C 235.4,707.21 235.57,707.21 235.57,707.37 C 235.57,707.55 235.41,707.55 235.31,707.55 L 233.18,707.55 L 233.18,709.69 C 233.18,709.78 233.18,709.95 233.01,709.95 C 232.84,709.95 232.84,709.79 232.84,709.69 L 232.84,707.55 L 230.7,707.55 C 230.61,707.55 230.44,707.55 230.44,707.38 C 230.44,707.21 230.6,707.21 230.7,707.21 L 232.84,707.21 L 232.84,705.07 C 232.84,704.97 232.84,704.81 233.01,704.81 C 233.18,704.81 233.18,704.97 233.18,705.07 L 233.18,707.21 z"
- style="fill:#000000;stroke-width:0" />
-</g> <g
id="g3661"
transform="matrix(1.2437811,0,0,-1.2437811,96.69279,1057.2544)"
xml:space="preserve"
@@ -292,30 +268,6 @@
id="path3667"
style="fill:#000000;stroke-width:0" />
</g> <g
- id="g5306"
- transform="matrix(1.5197568,0,0,-1.5197568,-170.5927,1335.7512)"
- xml:space="preserve"
- stroke-miterlimit="10.433"
- fill-rule="even-odd"
- font-style="normal"
- font-variant="normal"
- font-weight="normal"
- font-stretch="normal"
- font-size-adjust="none"
- letter-spacing="normal"
- word-spacing="normal"
- ns0:text="$\\varphi_-$"
- ns0:preamble=""
- style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
-<path
- d="M 225.13,705.43 L 225.12,705.42 L 225.12,705.42 L 225.12,705.41 L 225.12,705.41 L 225.12,705.4 L 225.12,705.4 L 225.11,705.39 L 225.11,705.38 L 225.11,705.37 L 225.1,705.36 L 225.1,705.35 L 225.1,705.34 L 225.1,705.34 L 225.09,705.33 L 225.09,705.32 L 225.09,705.32 L 225.09,705.31 L 225.09,705.3 L 225.09,705.3 L 225.08,705.29 L 225.08,705.29 L 225.08,705.28 L 225.08,705.28 L 225.08,705.28 L 225.08,705.27 L 225.08,705.26 L 225.08,705.26 L 225.08,705.25 L 225.08,705.24 L 225.08,705.23 L 225.08,705.23 C 225.08,705.01 225.27,704.95 225.37,704.95 C 225.41,704.95 225.63,704.98 225.73,705.21 C 225.76,705.29 225.81,705.62 226.08,707.03 C 226.17,707.02 226.24,707.01 226.41,707.01 C 228.07,707.01 229.6,708.58 229.6,710.15 L 229.32,709.93 C 229.32,708.81 228.04,707.59 226.5,707.59 L 226.5,707.59 C 226.42,707.59 226.4,707.59 226.32,707.6 C 226.2,707.6 226.19,707.61 226.19,707.64 C 226.19,707.66 226.36,708.57 226.39,708.72 C 226.7,709.99 227.48,710.95 228.36,710.95 C 229.05,710.95 229.32,710.41 229.32,709.93 L 229.6,710.15 C 229.6,710.93 229.21,711.53 228.46,711.53 C 227.02,711.53 226.42,709.59 225.82,707.65 C 224.75,707.85 224.19,708.41 224.19,709.12 C 224.19,709.4 224.42,710.5 225.02,711.19 C 225.1,711.28 225.1,711.3 225.1,711.32 C 225.1,711.36 225.08,711.42 224.98,711.42 C 224.7,711.42 223.93,709.97 223.93,709.02 C 223.93,708.08 224.59,707.35 225.65,707.1 L 225.13,705.43 z"
- id="path5308"
- style="fill:#000000;stroke-width:0" />
-<path
- d="M 235.16,707.21 L 235.17,707.21 L 235.18,707.21 L 235.19,707.21 L 235.2,707.21 L 235.21,707.21 L 235.22,707.21 L 235.23,707.21 L 235.24,707.21 L 235.25,707.21 L 235.26,707.21 L 235.27,707.21 L 235.28,707.21 L 235.29,707.22 L 235.3,707.22 L 235.31,707.22 L 235.32,707.23 L 235.33,707.23 L 235.34,707.24 L 235.35,707.24 L 235.36,707.25 L 235.37,707.25 L 235.38,707.26 L 235.38,707.27 L 235.39,707.27 L 235.39,707.28 L 235.39,707.28 L 235.4,707.29 L 235.4,707.29 L 235.4,707.3 L 235.4,707.3 L 235.41,707.31 L 235.41,707.31 L 235.41,707.32 L 235.41,707.32 L 235.41,707.33 L 235.41,707.34 L 235.42,707.34 L 235.42,707.35 L 235.42,707.36 L 235.42,707.37 L 235.42,707.37 C 235.42,707.55 235.26,707.55 235.16,707.55 L 230.96,707.55 C 230.86,707.55 230.7,707.55 230.7,707.37 C 230.7,707.21 230.87,707.21 230.96,707.21 L 235.16,707.21 z"
- id="path5310"
- style="fill:#000000;stroke-width:0" />
-</g> <g
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
ns0:preamble=""
ns0:text="$\\theta_+^-$"
@@ -543,5 +495,75 @@
d="M 259.64285,253.25503 L 258.64319,252.76075 L 259.57108,252.14216 L 259.64285,253.25503 z"
transform="matrix(2.474828,2.8604014,-2.8604014,2.474828,449.39876,-1188.7)" />
</g>
- </g>
+ <g
+ id="g2504"
+ transform="matrix(1.5197568,0,0,-1.5197568,-170.5927,1335.7512)"
+ xml:space="preserve"
+ stroke="black"
+ stroke-linecap="butt"
+ stroke-linejoin="miter"
+ stroke-miterlimit="10.433"
+ stroke-dasharray="none"
+ stroke-dashoffset="0"
+ stroke-opacity="1"
+ fill="none"
+ fill-rule="even-odd"
+ fill-opacity="1"
+ font-style="normal"
+ font-variant="normal"
+ font-weight="normal"
+ font-stretch="normal"
+ font-size-adjust="none"
+ letter-spacing="normal"
+ word-spacing="normal"
+ text-anchor="start"
+ ns0:text="$\\phi_-$"
+ ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1">
+<path
+ d="M227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.81 L227.79,713.81 L227.79,713.81 L227.79,713.82 L227.79,713.82 L227.79,713.83 L227.79,713.83 L227.79,713.84 L227.79,713.84 L227.8,713.85 L227.8,713.85 L227.8,713.86 L227.8,713.87 L227.8,713.88 L227.81,713.89 L227.81,713.89 L227.81,713.9 L227.81,713.9 L227.81,713.91 L227.81,713.91 L227.81,713.92 L227.81,713.92 L227.81,713.93 L227.81,713.93 L227.81,713.93 L227.81,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.94 L227.82,713.94 L227.82,713.94 C227.82,713.95,227.82,714.04,227.7,714.04 C227.6,714.04,227.59,714.01,227.55,713.84 L226.97,711.54 C225.38,711.49,223.92,710.16,223.92,708.81 C223.92,707.86,224.62,707.07,225.83,707 L225.88,707.22 C225.29,707.25,224.57,707.6,224.57,708.6 C224.57,709.79,225.43,711.19,226.91,711.32 L225.88,707.22 L225.83,707 C225.75,706.69,225.68,706.38,225.6,706.07 C225.49,705.6,225.38,705.22,225.38,705.19 C225.38,705.09,225.46,705.08,225.51,705.08 C225.55,705.08,225.57,705.09,225.6,705.12 C225.62,705.14,225.68,705.38,225.71,705.52 C225.84,706.01,225.96,706.51,226.09,707 L226.14,707.22 L227.17,711.32 C227.93,711.28,228.49,710.82,228.49,709.94 C228.49,708.77,227.64,707.34,226.14,707.22 L226.09,707 C227.7,707.05,229.14,708.4,229.14,709.73 C229.14,710.52,228.61,711.44,227.23,711.54 Z "
+ stroke-width="0"
+ fill="black"
+ id="path2506" />
+<path
+ d="M234.57,707.21 L234.58,707.21 L234.59,707.21 L234.6,707.21 L234.61,707.21 L234.62,707.21 L234.63,707.21 L234.64,707.21 L234.65,707.21 L234.66,707.21 L234.67,707.21 L234.68,707.21 L234.7,707.21 L234.71,707.22 L234.72,707.22 L234.73,707.22 L234.74,707.23 L234.75,707.23 L234.76,707.24 L234.77,707.24 L234.77,707.25 L234.78,707.25 L234.79,707.26 L234.8,707.27 L234.8,707.27 L234.8,707.28 L234.81,707.28 L234.81,707.29 L234.81,707.29 L234.82,707.3 L234.82,707.3 L234.82,707.31 L234.82,707.31 L234.82,707.32 L234.83,707.32 L234.83,707.33 L234.83,707.34 L234.83,707.34 L234.83,707.35 L234.83,707.36 L234.83,707.37 L234.83,707.37 C234.83,707.55,234.67,707.55,234.57,707.55 H230.38 C230.28,707.55,230.12,707.55,230.12,707.37 C230.12,707.21,230.29,707.21,230.38,707.21 Z "
+ stroke-width="0"
+ fill="black"
+ id="path2508" />
+</g> <g
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;letter-spacing:normal;word-spacing:normal;text-anchor:start;fill:none;fill-opacity:1;stroke:#000000;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10.43299961;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+ ns0:preamble="/home/mlenz/.inkscape/textext-preamble.tex"
+ ns0:text="$\\phi_+$"
+ text-anchor="start"
+ word-spacing="normal"
+ letter-spacing="normal"
+ font-size-adjust="none"
+ font-stretch="normal"
+ font-weight="normal"
+ font-variant="normal"
+ font-style="normal"
+ fill-opacity="1"
+ fill-rule="even-odd"
+ fill="none"
+ stroke-opacity="1"
+ stroke-dashoffset="0"
+ stroke-dasharray="none"
+ stroke-miterlimit="10.433"
+ stroke-linejoin="miter"
+ stroke-linecap="butt"
+ stroke="black"
+ xml:space="preserve"
+ transform="matrix(1.5197568,0,0,-1.5197568,-130.14647,1351.9304)"
+ id="content">
+<path
+ id="path2640"
+ fill="black"
+ stroke-width="0"
+ d="M227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.8 L227.79,713.81 L227.79,713.81 L227.79,713.81 L227.79,713.82 L227.79,713.82 L227.79,713.83 L227.79,713.83 L227.79,713.84 L227.79,713.84 L227.8,713.85 L227.8,713.85 L227.8,713.86 L227.8,713.87 L227.8,713.88 L227.81,713.89 L227.81,713.89 L227.81,713.9 L227.81,713.9 L227.81,713.91 L227.81,713.91 L227.81,713.92 L227.81,713.92 L227.81,713.93 L227.81,713.93 L227.81,713.93 L227.81,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.93 L227.82,713.94 L227.82,713.94 L227.82,713.94 C227.82,713.95,227.82,714.04,227.7,714.04 C227.6,714.04,227.59,714.01,227.55,713.84 L226.97,711.54 C225.38,711.49,223.92,710.16,223.92,708.81 C223.92,707.86,224.62,707.07,225.83,707 L225.88,707.22 C225.29,707.25,224.57,707.6,224.57,708.6 C224.57,709.79,225.43,711.19,226.91,711.32 L225.88,707.22 L225.83,707 C225.75,706.69,225.68,706.38,225.6,706.07 C225.49,705.6,225.38,705.22,225.38,705.19 C225.38,705.09,225.46,705.08,225.51,705.08 C225.55,705.08,225.57,705.09,225.6,705.12 C225.62,705.14,225.68,705.38,225.71,705.52 C225.84,706.01,225.96,706.51,226.09,707 L226.14,707.22 L227.17,711.32 C227.93,711.28,228.49,710.82,228.49,709.94 C228.49,708.77,227.64,707.34,226.14,707.22 L226.09,707 C227.7,707.05,229.14,708.4,229.14,709.73 C229.14,710.52,228.61,711.44,227.23,711.54 Z " />
+<path
+ id="path2642"
+ fill="black"
+ stroke-width="0"
+ d="M232.59,707.21 H234.73 C234.82,707.21,234.99,707.21,234.99,707.37 C234.99,707.55,234.83,707.55,234.73,707.55 H232.59 V709.69 C232.59,709.78,232.59,709.95,232.43,709.95 C232.25,709.95,232.25,709.79,232.25,709.69 V707.55 H230.11 C230.02,707.55,229.85,707.55,229.85,707.38 C229.85,707.21,230.01,707.21,230.11,707.21 H232.25 V705.07 C232.25,704.97,232.25,704.81,232.42,704.81 C232.59,704.81,232.59,704.97,232.59,705.07 Z " />
+</g> </g>
</svg>
View
4 tex/summary.tex
@@ -26,6 +26,10 @@ \chapter{Summary and Outlook}
In both cases a large angle between the incident beam the interface is
essential for obtaining a decent spin polarization.
+We also pointed out that experimental realization is quite possible, and that
+similar (but slightly more complex) setups have been grown and etched in HgTe
+quantum wells.
+
Future work in this area could involve a four-band model which includes both
the conductance and valance band for each spin direction, would
allow more precises modeling of a particular semiconductor, and thus be of
View
16 tex/thesis.tex
@@ -188,8 +188,6 @@ \section{Transmission and Green's Functions}
$\delta = \delta(x - x_0)$ to result in two waves propagating away from $x_0$,
so our ansatz is
-% TODO: explicit form of $H$
-
\begin{align}
G(x, x_0) = \begin{cases}
A^+ e^{i k(x-x_0) } \qquad \textnormal{ for } x > x_0 \\
@@ -370,6 +368,17 @@ \section{Rashba Spin-Orbit Coupling}
$m^*$ is the effective mass
and $\alpha$ denotes the strength of the spin-orbit coupling.
+\begin{figure}[tb]
+ \begin{center}
+ \includegraphics[height=0.5\textwidth]{rashba-dispersion.jpg}
+ \end{center}
+ \caption{The Rashba spin-orbit coupling lifts the spin degeneracy of the
+ dispersion relation $E(k)$for $k != 0$.
+ Image courtesy by M. Mühlbauer \cite{mathias}.
+ }
+ \label{fig:rashba-dispersion}
+\end{figure}
+
This effect lifts the degeneracy of spin-up and spin-down electrons for
$k \not= 0$:
@@ -380,7 +389,8 @@ \section{Rashba Spin-Orbit Coupling}
So the Rashba spin-orbit coupling splits the spin bands similarly as the Zeeman
effect of a
magnetic field, but it depends on the wave vector and does not come with the
-something that is equivalent to the Lorentz force of the magnetic field.
+something that is equivalent to the Lorentz force of the magnetic field (see
+figure \ref{fig:rashba-dispersion}) .
Since in equilibrium the same number of charge carries have the wave vectors
$k$ and $-k$, the Rashba spin-orbit coupling does not introduce a spin

0 comments on commit 968aa66

Please sign in to comment.