Class Syllabus

Welcome to Statistical Mechanics! The basic plan for the course is outlined below. I will draw from my own lecture notes and the books listed on the home page. In addition, the course texts are on reserve in the POA library that you may wish to consult.

Grades. There will be homework (40%), a midterm (25%), and final (35%).

Tentative plan for the course:

Topic 1 - Postulates of classical thermodynamics, entropy, temperature, pressure, chemical potential

Topic 2 - Conditions for thermal, mechanical and chemical equilibrium; concavity of the entropy, the Euler relation, equations of state, the Gibb-Duhem relation, entropy of the ideal gas

Topic 3 - Energy minimum principle, Legendre transformations, Helmholtz free energy

Topic 4 - Enthalpy, Gibbs free energy, Grand Potential, heat reservoir, extremum principles for thermodynamic potentials, Maxwell's relations

Topic 5 - Response functions (specific heat, compressibility, thermal expansion) and relations between them, stability and curvature of free energies

Topic 6 - Kinetic theory of the ideal gas, Maxwell's velocity distribution, statistical ensembles and the ergodic hypothesis

Topic 7 - Liouville's theorem, microcanonical ensemble, density of states and number of states, connection to entropy

Topic 8 - Entropy of the ideal gas, entropy of mixing and Gibbs paradox, indistinguishable particles, Sackur-Tetrode equation

Topic 9 - Canonical ensemble, energy fluctuation and specfi.c heat, equivalence of microcanonical and canonical ensembles

Topic 10 - Average energy vs most probable energy, proof of Stirling's formula, factorization of canonical partition function for non-interacting particles, ideal gas

Topic 11 - Virial and equipartition theorems, elastic vibrations of solids and the Law of Dulong and Petit, paramagnetism and the Curie Law

Topic 12 - Entropy and information theory

Topic 13 - The grand canonical ensemble, fluctuations of energy and number of particles

Topic 14 - The grand canonical partition function for non-interacting degrees of freedom, chemical equilibrium, absorption sites

Topic 15 - The density operator and quantum ensembles

Topic 16 - Quantum many particle systems, symmetry of the wavefunction, boson and fermions, non-interacting particles

Topic 17 - Two particle density matrix in real space, N particle partition function in real space representation, grand canonical partition function for non-interacting fermions and bosons

Topic 18 - Average occupation numbers, comparison with and validity of the classical limit of a quantum ideal gas, the harmonic oscillator and bosons

Topic 19 - Debye model for the speci.c heat due to ionic vibrations, black body radiation

Topic 20 - Ideal quantum gas of fermions or bosons, density, pressure, energy, classical limit

Topic 21 - Degenerate fermi gas, Sommerfeld model of electrons in a metal, Fermi energy, speci.c heat

Topic 22 - Pauli paramagnetism of an ideal fermi gas

Topic 23 - Ideal gas of bosons, Bose-Einstein condensation

Topic 24 - Bose-Einstein condensation in laser cooled atomic gases, classical spin models and ensembles

Topic 25 - Ising model, phase transitions and the thermodynamic limit, phase diagram

Topic 26 - Mean field approximation for the Ising model, graphical solution

Topic 27 - Critical exponents, Maxwell construction, Landau's theory of phase transitions

Topic 28 - Advanced topics