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incorporate lecture 18 notes.

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1 parent 2dc61fb commit 31543df697fe03af7f9919a7bcd2b10cb1dc3951 @peeterjoot committed Mar 26, 2013
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@@ -7,8 +7,8 @@ confocal
ParametericPlot
Indistinguishability
Exponentiating
-Fick's
Ficks
+Fick's
cgs
phasor
linestyle
@@ -87,8 +87,8 @@ Eikonal
Goldstein's
GPS
colinear
-Hmm
hoc
+Hmm
Peeter's
Benard
ijk
@@ -160,8 +160,8 @@ Hestenes's
parametrizations
imaginaries
reparametrize
-nlm
n'l'm
+nlm
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
-dj
BT
+dj
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
-KE
jj
+KE
elastostatics
amino
-jk
ip
+jk
indices
kj
-kk
iu
+kk
mc
mE
iz
@@ -377,8 +377,8 @@ Strang's
xyz
mk
resistive
-kx
mn
+kx
Eulerian
anticommutes
n'l
View
@@ -3031,15 +3031,15 @@ my @phy452 =
}
,{
SOURCE => 'kittleCh5Pr6',
- TITLE => qq(\generatetitle{Gibbs sum for a two level system}),
+ TITLE => qq(Gibbs sum for a two level system),
DATE => 'March 17, 2013',
REF => 'kittleCh5Pr6',
URL => 'http://sites.google.com/site/peeterjoot2/math2013/kittleCh5Pr6.pdf',
WHAT => qq()
}
,{
SOURCE => 'pathriaDiatomic',
- TITLE => qq(\generatetitle{Pathria chapter 4 diatomic molecule problem}),
+ TITLE => qq(Pathria chapter 4 diatomic molecule problem),
DATE => 'March 18, 2013',
REF => 'pathriaDiatomic',
URL => 'http://sites.google.com/site/peeterjoot2/math2013/pathriaDiatomic.pdf',
@@ -3069,6 +3069,14 @@ my @phy452 =
URL => 'http://sites.google.com/site/peeterjoot2/math2013/basicStatMechLecture17.pdf',
WHAT => qq()
}
+,{
+ SOURCE => 'basicStatMechLecture18',
+ TITLE => qq(Fermi gas thermodynamics),
+ DATE => 'March 26, 2013',
+ REF => 'basicStatMechLecture18',
+ URL => 'http://sites.google.com/site/peeterjoot2/math2013/basicStatMechLecture18.pdf',
+ WHAT => qq()
+}
) ; # @phy452
my @phy454 =
@@ -5272,3 +5280,4 @@ sub printHistory
+
@@ -2,24 +2,24 @@
% 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}{basicStatMechLecture18}
-\renewcommand{\dirname}{notes/phy452/}
-\newcommand{\keywords}{Statistical mechanics, PHY452H1S, Fermi gas, specific heat, density of states, graphene, relativisitic gas, chemical potential, energy, Fermi distribution, hole, electron}
-\input{../peeter_prologue_print2.tex}
-
-\beginArtNoToc
-\generatetitle{PHY452H1S Basic Statistical Mechanics. Lecture 18: Fermi gas thermodynamics. Taught by Prof.\ Arun Paramekanti}
+%\input{../blogpost.tex}
+%\renewcommand{\basename}{basicStatMechLecture18}
+%\renewcommand{\dirname}{notes/phy452/}
+%\newcommand{\keywords}{Statistical mechanics, PHY452H1S, Fermi gas, specific heat, density of states, graphene, relativistic gas, chemical potential, energy, Fermi distribution, hole, electron}
+%\input{../peeter_prologue_print2.tex}
+%
+%\beginArtNoToc
+%\generatetitle{PHY452H1S Basic Statistical Mechanics. Lecture 18: Fermi gas thermodynamics. Taught by Prof.\ Arun Paramekanti}
%\chapter{Fermi gas thermodynamics}
\label{chap:basicStatMechLecture18}
-\section{Disclaimer}
-
-Peeter's lecture notes from class. May not be entirely coherent.
-
+%\section{Disclaimer}
+%
+%Peeter's lecture notes from class. May not be entirely coherent.
+%
\paragraph{Review}
-Last time we found that the low temperature behaviour or the chemical potential was quadratic as in \cref{fig:lecture18:lecture18Fig1}.
+Last time we found that the low temperature behavior or the chemical potential was quadratic as in \cref{fig:lecture18:lecture18Fig1}.
\begin{dmath}\label{eqn:basicStatMechLecture18:20}
\mu =
@@ -28,7 +28,7 @@ \section{Disclaimer}
%\kB T ?
\end{dmath}
-\imageFigure{lecture18Fig1}{Fermi gas chemical potential}{fig:lecture18:lecture18Fig1}{0.2}
+\imageFigure{figures/lecture18Fig1}{Fermi gas chemical potential}{fig:lecture18:lecture18Fig1}{0.2}
\paragraph{Specific heat}
@@ -62,8 +62,8 @@ \section{Disclaimer}
The only change in the distribution \cref{fig:lecture18:lecture18Fig2}, that is of interest is over the step portion of the distribution, and over this range of interest $N(\epsilon)$ is approximately constant as in \cref{fig:lecture18:lecture18Fig3}.
-\imageFigure{lecture18Fig2}{Fermi distribution}{fig:lecture18:lecture18Fig2}{0.2}
-\imageFigure{lecture18Fig3}{Fermi gas density of states}{fig:lecture18:lecture18Fig3}{0.2}
+\imageFigure{figures/lecture18Fig2}{Fermi distribution}{fig:lecture18:lecture18Fig2}{0.2}
+\imageFigure{figures/lecture18Fig3}{Fermi gas density of states}{fig:lecture18:lecture18Fig3}{0.2}
\begin{subequations}
\begin{dmath}\label{eqn:basicStatMechLecture18:120}
@@ -88,7 +88,7 @@ \section{Disclaimer}
\lr{ n_{\mathrm{F}}(\epsilon + x, T) - n_{\mathrm{F}}(\epsilon_{\mathrm{F}} + x, 0)}.
\end{dmath}
-Here we've made a change of variables $\epsilon = \epsilon_{\mathrm{F}} + x$, so that we have near cancelation of the $\epsilon_{\mathrm{F}}$ factor
+Here we've made a change of variables $\epsilon = \epsilon_{\mathrm{F}} + x$, so that we have near cancellation of the $\epsilon_{\mathrm{F}}$ factor
\begin{dmath}\label{eqn:basicStatMechLecture18:180}
\Delta e
@@ -227,12 +227,12 @@ \section{Disclaimer}
This is illustrated in \cref{fig:lecture18:lecture18Fig4}.
-\imageFigure{lecture18Fig4}{Specific heat per Fermion}{fig:lecture18:lecture18Fig4}{0.25}
+\imageFigure{figures/lecture18Fig4}{Specific heat per Fermion}{fig:lecture18:lecture18Fig4}{0.25}
-\paragraph{Relativisitic gas}
+\paragraph{Relativistic gas}
\begin{itemize}
-\item Relativisitic gas
+\item Relativistic gas
\begin{dmath}\label{eqn:basicStatMechLecture18:340}
\epsilon_\Bk = \pm \hbar v \Abs{\Bk}.
@@ -246,11 +246,11 @@ \section{Disclaimer}
\item massless Dirac Fermion
%\cref{fig:lecture18:lecture18Fig5}.
-\imageFigure{lecture18Fig5}{Relativisitic gas energy distribution}{fig:lecture18:lecture18Fig5}{0.3}
+\imageFigure{figures/lecture18Fig5}{Relativistic gas energy distribution}{fig:lecture18:lecture18Fig5}{0.3}
-We can think of this state distribution in a condensed matter view, where we can have a hole to electron state transition by supplying energy to the system (i.e. shining light on the substrate). This can also be thought of in a relativisitic particle view where the same state transition can be thought of as a positron electron pair transition. A round trip transition will have to supply energy like $2 m_0 c^2$ as illustrated in \cref{fig:lecture18:lecture18Fig6}.
+We can think of this state distribution in a condensed matter view, where we can have a hole to electron state transition by supplying energy to the system (i.e. shining light on the substrate). This can also be thought of in a relativistic particle view where the same state transition can be thought of as a positron electron pair transition. A round trip transition will have to supply energy like $2 m_0 c^2$ as illustrated in \cref{fig:lecture18:lecture18Fig6}.
-\imageFigure{lecture18Fig6}{Hole to electron round trip transition energy requirement}{fig:lecture18:lecture18Fig6}{0.2}
+\imageFigure{figures/lecture18Fig6}{Hole to electron round trip transition energy requirement}{fig:lecture18:lecture18Fig6}{0.2}
\end{itemize}
@@ -264,7 +264,7 @@ \section{Disclaimer}
We'll find a density of states distribution like \cref{fig:lecture18:lecture18Fig7}.
-\imageFigure{lecture18Fig7}{Density of states for 2D linear energy momentum distribution}{fig:lecture18:lecture18Fig7}{0.2}
+\imageFigure{figures/lecture18Fig7}{Density of states for 2D linear energy momentum distribution}{fig:lecture18:lecture18Fig7}{0.2}
\begin{dmath}\label{eqn:basicStatMechLecture18:400}
N(\epsilon) = \text{constant factor} \frac{\Abs{\epsilon}}{v},
@@ -304,5 +304,4 @@ \section{Disclaimer}
C_{\mathrm{Dimensionless}} \sim T^2
\end{dmath}
-%\EndArticle
-\EndNoBibArticle
+%\EndNoBibArticle
@@ -93,6 +93,7 @@ \part{Lecture Notes}
\input{basicStatMechLecture15.tex}
\section{Fermi gas thermodynamics}
\input{basicStatMechLecture17.tex}
+ \input{basicStatMechLecture18.tex}
\section{Problems}
\input{entropyProbabilityForm.tex}
\input{varianceN.tex}

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