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PHY 418: Statistical Mechanics I
Prof. S. Teitel stte@pas.rochester.edu  Spring 2012
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 guarantees 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 0  Sketching the history of statistical mechanics and thermodynamics (another such page here.)
 Lecture 1  Postulates of classical thermodynamics, entropy, temperature, pressure, chemical potential, condition for thermal equilibrium
 Lecture 2  Conditions for mechanical and chemical equilibrium, concavity of the entropy, equations of state, Euler relation, GibbsDuhem relation
 Lecture 3  Entropy of the ideal gas, entropy maximum vs energy minimum principle, Legendre transformation
 Lecture 4  Helmholtz and Gibbs free energies, enthalpy, the grand potential, reservoirs, extremum principles for these new thermodynamic potentials
 Lecture 5  Maxwell relations, response functions and relations between them
 Lecture 6  Curvature of free energies and stability requirements for response functions, kinetic theory of ideal gas, Maxwell velocity distribution
Lecture 6 supplement  Heat engines, thermodynamic efficiency, Carnot cycle
 Lecture 7  Ergodic hypothesis, statisitcal ensembles, density matrix, Liouville's theorem, microcanonical ensemble, density of states
 Lecture 8  Density of states and connection to entropy, entropy of the ideal gas and problem of extensivity, entropy of mixing and Gibbs' paradox
 Lecture 9  Entropy of mixing continued, indistinguishable particles, the canonical ensemble and the canonical partition function
 Lecture 10  Helholtz free energy and the canonical partition function, energy fluctuations, equivalence of canonical and microcanonical ensembles in the thermodynamic limit
 Lecture 11  Average energy vs most probably energy, Stirling's formula, factoring the canonical partition function for noninteracting objects, Maxwell velocity distribution revisited
 Lecture 12  The virial theorm, the equipartition theorem, elastic vibrations of a solid and the law of Dulong and Petit, paramagnetism of classical spins and the Curie law of paramagnetic susceptibility
 Lecture 13  Entropy and information
 Lecture 14  The grand canonical ensemble: the grand canonical partition function and the grand potential, fluctuations in the number of particles
 Lecture 15  Fluctuations in the grand canonical ensemble continued, the grand canonical partition function for noninteracting particles, chemical equilibrium, a gas in equilibrium with a surface of absorption sites
 Lecture 16  A gas in equilibrium with an absorbing surface, quantum ensembles, density matrix
 Lecture 17  Quantum microcanonical, canonical, and grand canonical ensembles, quantum harmonic osciallator at temperature T, BoseEinstein and FermiDirac statistics, Pauli exlusion principle, occupation number representation, density matrix for two noninteracting particles
 Lecture 18  Two particle density matrix continued, quantum correlations as an effective classical pair interaction, Nparticle partition function in the positionspace basis, partition functions for noninteracting quantum ideal gas
 Lecture 19  Classical partition function in the occupation number representation, average occupation number, the classical vs quantum limits of the ideal gas, the quantized harmonic oscillator as bosons
 Lecture 20  Debye model for the specific heat of a solid, black body radiation
 Lecture 21  The quantum ideal gas, standard functions, pressure, density, energy, the leading correction to the classical limit
 Lecture 22  The degenerate Fermi gas, ground state energy, the Sommerfeld expansion, chemical potential at finite temperature, specific heat, Pauli paramagnetism
 Lecture 23  Pauli paramagnetism continued, ideal Bose gas
 Lecture 24  BoseEinstein condensation in an ideal gas of free bosons
 Lecture 25  BEC in laser cooled atomic gases, classical spin models, constant magnetization vs constant magnetic field ensembles
 Lecture 26  Broken symmetry and the possibility for a phase transition in the thermodynamic limit, Ising phase diagram
 Lecture 27  Meanfield solution of the Ising model, critical exponents
 Lecture 28  Meanfield solution and critical exponents continued, Maxwell construction, Landau theory of phase transitions, the liquidgas transition
Lecture 29  Landau theory continued, critical exponents, specific heat, exact solution of one dimensional Ising model
 Lecture 30  Fluctuations and diverging length scale at a 2nd order critical point, LandauGinzburg theory, correlation functions, upper and lower critical dimensions

