Lecture Notes

Lecture Notes

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, Gibbs-Duhem 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 non-interacting 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 non-interacting 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, Bose-Einstein and Fermi-Dirac statistics, Pauli exlusion principle, occupation number representation, density matrix for two non-interacting particles
Lecture 18 - Two particle density matrix continued, quantum correlations as an effective classical pair interaction, N-particle partition function in the position-space basis, partition functions for non-interacting 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 - Bose-Einstein 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 - Mean-field solution of the Ising model, critical exponents
Lecture 28 - Mean-field solution and critical exponents continued, Maxwell construction, Landau theory of phase transitions, the liquid-gas 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, Landau-Ginzburg theory, correlation functions, upper and lower critical dimensions