

Home
Contact Info
Course Info
Calendar
Homework
Lecture Notes




Physics 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu  Spring 2006
Lecture Notes
My hand written class lecture notes are being scanned and uploaded for you to view. Please be warned that these are the notes I prepare for myself to lecture from  they are not in general carefully prepared for others to read. I make no guarentees about their legibility, or that they are totally free of errors. I hope, nevertheless that you will find them useful. The lectures are uploaded as pdf files, so you will need Adobe Acrobat Reader in order to read them. You can download Acrobat Reader for free here.
The lecture note files correspond roughly to the material presented in a given day's lecture. But you may on occassion find the end of one day's lecture at the start of the file for the next day's lecture, so please look there if you think there might be something missing.
 Lecture 1 
Postulates of classical thermodynamics; extensive and intensive variables
 Lecture 2 
Thermal, mechanical and chemical equilibrium; concavity of the entropy; Euler relation; equations of state; GibbsDuhem relation
 Lecture 3 
Entropy of the ideal gas; energy minimum principal
 Lecture 4 
Legendre transformations; Helmholtz free energy, enthalpy, Gibbs free energy and the grand potential
 Lecture 5 
Extrema principals for various thermodynamic potentials; reservoirs; Maxwell relations;
response functions and relations among them
 Lecture 6 
Thermodynamic stability within various potentials and consequences for response functions; kinetic theory of the ideal gas and Maxwell velocity distribution; statistical ensembles and the ergodic hypothesis
 Lecture 7 
Liouville's Theorem; microcanonical and canonical ensemble, density of states; connection to entropy
 Lecture 8 
Entropy of the ideal gas revisited; entropy of mixing and Gibbs parodox; indistiguishable particles
 Lecture 9 
The canonical ensemble; energy fluctuations
 Lecture 10 
Equivalence of the canonical and microcanonical ensembles in the thermodynamic limit; ideal gas in the canonical ensemble; virial and equipartition theorems.
 Lecture 11 
Elastic vibartions of a solid and the Law of Dulong and Petit; Curie Law for paramagnetism; entropy and information
 Lecture 12 
Entropy and information continued
 Lecture 13 
The grand canonical ensemble
 Lecture 14 
The grand canonical ensemble for noninteracting particles; chemical equilibrium
 Lecture 15 
Quantum ensembles; the density matrix
 Lecture 16 
Many particle quantum systems; FermiDirac and BoseEinstein statistics; noninteracting particles; two particle density matrix and effective interaction
 Lecture 17 
Nparticle canonical partition function in real space representation; corrections to classical result due to particle exchanges; the grand canonical partition function for noninteracting fermions, bosons, and classical particles
 Lecture 18 
Average occupation numbers; comparision of quantum vs classical single particle partition function; the classical limit; harmonic oscillator vs bosons
 Lecture 19 
Debye model for the specific heat of a solid; black body radiation and StefanBoltzmann Law
 Lecture 20 
Ideal quantum gas of fermions or bosons; the "standard" functions; nondegenerate limit and leading quantum corrections to the ideal gas equation of state; degenerate fermi gas and the Sommerfeld model of electrons in a conductor
 Lecture 21 
Degenerate ideal fermi gas: Sommerfeld expansion (not covered in class); specific heat; Pauli paramagnetism
 Lecture 22 
Degenerate ideal bose gas: BoseEinstein condensation
 Lecture 23 
BoseEinstein condensation continued; BEC of laser cooled gases in magnetic traps
 Lecture 24 
Classical spin models; magnetic ensembles; phase transitions and the thermodynamic limit; phase diagram for the Ising model
 Lecture 25 
Mean field solution of the Ising model; critical exponents
 Lecture 26 
Landau theory of phase transition
 Lecture 27 
Critical exponents within Landau theory; exact solution of one dimensional Ising model
 Lecture 28 
LandauGinzburg theory  including fluctuations; correlation function; fluctuation corrections to specific heat; upper critical dimension
