Syllabus
* A. Fundamentals of statistical mechanics
* Classical statistical mechanics
Macroscopic and microscopic states, ergodic systems and thermodynamic limit. Microcanonical ensemble, equipartition and virial theorem, Gibbs paradox. Canonical and great canonical ensemble, thermodynamic potentials, homogeneity.
* Quantum statistical mechanics
Postulates of quantum statistical mechanics, density matrix, statistical ensembles, the third law of thermodynamics, statistical sum, the saddle point method, the classical limit, ideal quantum gases, Bose and Fermi distribution
* The theory of fluctuations and equivalence of statistical ensembles
Moments of distribution functions, correlation functions, quadratic correlations, Gibbs and Einstein's method, thermodynamic limit and equivalence of statistical ensembles, the relation of thermodynamics and statistical mechanics.
* Ideal Bose-Einstein gas
Chemical potential, Bose-Einstein condensation, superfluidity, the phonon gas, Einstein-Debye model of solids, photon gas, black body radiation.
* The ideal Fermi-Dirac gas
Equation of state, limit cases, nonrelativistic electron gas, Sommerfeld expansion; relativistic electron gas, white dwarfs, spin and magnetism.
* B. Selected problems of statistical mechanics
* Gas of classical interacting particles
Interacting dilute gas, classical cluster, group, and virial expansion.
* Basic theory of phase transitions
Singularity in the statistical sum, Lee-Young's theorems, phase transitions, order parameter, correlation functions, critical exponents, Landau mean field theory, the scaling hypothesis, universality and renormalization group.
* Fundamentals of nonequilibrium statistical physics
Evolution equations for nonequilibrium ensemble (BBGKY equations), the kinetic Boltzmann equation, Boltzmann H theorem. Correlation functions and response functions, fluctuation-dissipation theorem.
Annotation
Thermodynamic limit, Gibbs paradox. Identical particles, quantum statistical ensembles, the classical limit.
Fluctuation theory, equivalence of statistical ensembles. Ideal Bose and Fermi gas. Interacting systems: virial expansion, critical phenomena, mean field approximation, the scaling hypothesis. Transport phenomena,
Boltzmann kinetic equation. For the 3rd year of the TF study.