Thermodynamics and Statistical Mechanics on the Qualifier

**I-3. THERMODYNAMICS, KINETIC THEORY, and CLASSICAL GASES **

Refs: R.K.Pathria & P.D. Beale, Statistical Mechanics; M. Kardar, Statistical Physics of Fields; S.J. Blundell & K.M. Blundell, Concepts in Thermal Physics:

- Thermodynamics: Microscopic/macroscopic variables, extensivity, first and second laws, thermodynamic potentials, Legendre transformations, thermodynamics relations, Maxwell relations, Clausius-Clapeyron, Maxwell construction, phase coexistence, entropy of mixing, chemical equilibrium
- Kinetic theory: Maxwell-Boltzmann speed distribution, pressure, effusion
- Foundations of statistical mechanics: classical mechanics: Hamiltonian, phase space, ergodic approach, ensemble approach, microcanonical postulate, canonical and grand-canonical ensembles, classical ideal gas, fluctuations of energy and particle number.
- Introductory Applications: Ideal gas of particles, specific heats, ortho-para- H 2 , third law of thermodynamics, imperfect gases and fluids, virial expansion, Mayer's cluster idea, correlation functions, density fluctuations and compressibility.

II-5. **QUANTUM STATISTICAL MECHANICS AND PHASE TRANSITIONS **,

Refs: R.K.Pathria & P.D. Beale, Statistical Mechanics; M. Kardar, Statistical Physics of Fields; S.J. Blundell & K.M. Blundell, Concepts in Thermal Physics:

Formulation of quantum statistical mechanics, density matrices; Bose gase, ideal Bose gas, Bose-Einstein condensation, applications to superfluids and ultracold atoms; blackbody radiation, ideal crystals, Einstein model, normal modes, Debye model, T 3 -law; Fermi gas: Fermi surface in free space and in a crystal, paramagnetism, Landau diamagnetism, Curie's law, use of Sommerfeld expansion. Interacting Ising spins, transfer-matrix method in 1D, mean field theory, Landau theory of phase transitions, order parameter, metastability; Role of spatial and order-parameter dimensionality.