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move L19 into collection.

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1 parent a0ca58e commit 7617e8f3ee8d24a10d0e9e91d5631de01b98bdf3 @peeterjoot committed Mar 28, 2013
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@@ -7,8 +7,8 @@ confocal
ParametericPlot
Indistinguishability
Exponentiating
-Ficks
Fick's
+Ficks
cgs
phasor
linestyle
@@ -87,8 +87,8 @@ Eikonal
Goldstein's
GPS
colinear
-hoc
Hmm
+hoc
Peeter's
Benard
ijk
@@ -160,8 +160,8 @@ Hestenes's
parametrizations
imaginaries
reparametrize
-n'l'm
nlm
+n'l'm
PDE
Lut
quantized
@@ -188,8 +188,8 @@ arctan
entropic
invertible
pion
-outermorphism
OuterMorphism
+outermorphism
QFT
rescaling
spinors
@@ -310,8 +310,8 @@ df
LIGO
spacetime
dH
-BT
dj
+BT
Routhian
dk
dL
@@ -339,9 +339,9 @@ Prandtl
ia
isync
inferometer
-eV
ib
iB
+eV
orthonormalization
ic
ie
@@ -355,16 +355,16 @@ variates
im
Dekker's
ji
-jj
KE
+jj
elastostatics
amino
-ip
jk
+ip
indices
kj
-iu
kk
+iu
mc
mE
iz
@@ -377,8 +377,8 @@ Strang's
xyz
mk
resistive
-mn
kx
+mn
Eulerian
anticommutes
n'l
View
@@ -3085,6 +3085,14 @@ my @phy452 =
URL => 'http://sites.google.com/site/peeterjoot2/math2013/basicStatMechLecture16.pdf',
WHAT => qq()
}
+,{
+ SOURCE => 'basicStatMechLecture19',
+ TITLE => qq(Bosons),
+ DATE => 'March 28, 2013',
+ REF => 'basicStatMechLecture19',
+ URL => 'http://sites.google.com/site/peeterjoot2/math2013/basicStatMechLecture19.pdf',
+ WHAT => qq()
+}
) ; # @phy452
my @phy454 =
@@ -5291,3 +5299,4 @@ sub printHistory
}
}
+
@@ -2,27 +2,27 @@
% Copyright © 2013 Peeter Joot. All Rights Reserved.
% Licenced as described in the file LICENSE under the root directory of this GIT repository.
%
-\input{../blogpost.tex}
-\renewcommand{\basename}{basicStatMechLecture19}
-\renewcommand{\dirname}{notes/phy452/}
-\newcommand{\keywords}{Statistical mechanics, PHY452H1S, Boson, Bose condensate, fugacity, occupation number, density, zeta function}
-\input{../peeter_prologue_print2.tex}
-
-\beginArtNoToc
-\generatetitle{PHY452H1S Basic Statistical Mechanics. Lecture 19: Bosons. Taught by Prof.\ Arun Paramekanti}
-%\chapter{Bosons}
-\label{chap:basicStatMechLecture19}
-
-\section{Disclaimer}
-
-Peeter's lecture notes from class. May not be entirely coherent.
+%\input{../blogpost.tex}
+%\renewcommand{\basename}{basicStatMechLecture19}
+%\renewcommand{\dirname}{notes/phy452/}
+%\newcommand{\keywords}{Statistical mechanics, PHY452H1S, Boson, Bose condensate, fugacity, occupation number, density, zeta function}
+%\input{../peeter_prologue_print2.tex}
+%
+%\beginArtNoToc
+%\generatetitle{PHY452H1S Basic Statistical Mechanics. Lecture 19: Bosons. Taught by Prof.\ Arun Paramekanti}
+%%\chapter{Bosons}
+%\label{chap:basicStatMechLecture19}
+%
+%\section{Disclaimer}
+%
+%Peeter's lecture notes from class. May not be entirely coherent.
-\section{Fermions summary}
+\paragraph{Summary of our Fermion approach}
We've considered a momentum sphere as in \cref{fig:lecture19:lecture19Fig1}, and performed various appromations of the occupation sums \cref{fig:lecture19:lecture19Fig2}.
-\imageFigure{lecture19Fig1}{Summation over momentum sphere}{fig:lecture19:lecture19Fig1}{0.3}
-\imageFigure{lecture19Fig2}{Fermion occupation}{fig:lecture19:lecture19Fig2}{0.3}
+\imageFigure{figures/lecture19Fig1}{Summation over momentum sphere}{fig:lecture19:lecture19Fig1}{0.3}
+\imageFigure{figures/lecture19Fig2}{Fermion occupation}{fig:lecture19:lecture19Fig2}{0.3}
\begin{subequations}
\begin{dmath}\label{eqn:basicStatMechLecture19:20}
@@ -44,7 +44,7 @@ \section{Fermions summary}
\item Ultracold atomic gases: $T_{\mathrm{F}} \sim (10 - 100) \mbox{n K}$
\end{itemize}
-\section{Bosons}
+\paragraph{Moving on to Bosons}
We'd like to work with a fixed number of particles, but the calculations are hard, so we move to the grand canonical ensemble
@@ -58,7 +58,7 @@ \section{Bosons}
\epsilon_\Bk = \frac{\hbar^2 k^2}{2 m}.
\end{dmath}
-\imageFigure{lecture19Fig3}{Free particle energy momentum distribution}{fig:lecture19:lecture19Fig3}{0.3}
+\imageFigure{figures/lecture19Fig3}{Free particle energy momentum distribution}{fig:lecture19:lecture19Fig3}{0.3}
Again introducing fugacity $z = e^{\beta \mu}$, we have
@@ -85,7 +85,7 @@ \section{Bosons}
Observe that we require $z < 1$ (or $\mu < 0$) so that the number distribution is strictly positive for all energies. This tells us that the fugacity is a function of temperature, but there will be a point at which it must saturate. This is illustrated in \cref{fig:lecture19:lecture19Fig4}.
-\imageFigure{lecture19Fig4}{Density times cubed thermal de Broglie wavelength}{fig:lecture19:lecture19Fig4}{0.3}
+\imageFigure{figures/lecture19Fig4}{Density times cubed thermal de Broglie wavelength}{fig:lecture19:lecture19Fig4}{0.3}
Let's calculate this density (assumed fixed for all temperatures)
@@ -202,7 +202,7 @@ \section{Bosons}
as in \cref{fig:lecture19:lecture19Fig6}, so that
-\imageFigure{lecture19Fig6}{Momentum sphere with origin omitted}{fig:lecture19:lecture19Fig6}{0.3}
+\imageFigure{figures/lecture19Fig6}{Momentum sphere with origin omitted}{fig:lecture19:lecture19Fig6}{0.3}
\begin{dmath}\label{eqn:basicStatMechLecture19:420}
\sum_\Bk
@@ -219,7 +219,7 @@ \section{Bosons}
We can illustrate this as in \cref{fig:lecture19:lecture19Fig7}.
-\imageFigure{lecture19Fig7}{Boson occupation vs momentum}{fig:lecture19:lecture19Fig7}{0.3}
+\imageFigure{figures/lecture19Fig7}{Boson occupation vs momentum}{fig:lecture19:lecture19Fig7}{0.3}
\begin{dmath}\label{eqn:basicStatMechLecture19:420c}
\rho
@@ -235,5 +235,4 @@ \section{Bosons}
At $T > T_{\mathrm{c}}$ we have $\rho_{\Bk = 0}$, whereas at $T < T_{\mathrm{c}}$ we must introduce a non-zero density if we want to be able to keep a constant density constraint.
-%\EndArticle
-\EndNoBibArticle
+%\EndNoBibArticle
@@ -95,6 +95,8 @@ \part{Lecture Notes}
\input{basicStatMechLecture16.tex}
\input{basicStatMechLecture17.tex}
\input{basicStatMechLecture18.tex}
+ \section{Bosons}
+ \input{basicStatMechLecture19.tex}
\section{Problems}
\input{entropyProbabilityForm.tex}
\input{varianceN.tex}

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