Statistical mechanics
Graduate · Physics
Syllabus focus
Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Theoretical / proof-based
Ensemble theory
- Liouville equation and BBGKY hierarchy (intro)
- Cumulant expansion and cluster integrals
- Quantum partition functions and density matrices
- Grand potentials and fugacity expansions
- Linear response and Kubo formulas
Phase transitions
- Landau–Ginzburg theory and order parameters
- Ising model: exact 2D solution and mean field
- Critical exponents and scaling laws
- Renormalization group on lattices
- Kosterlitz–Thouless transition (overview)
Advanced systems
- Bose–Einstein condensation in trapped gases
- Fermi liquids and quasiparticles
- Spin models and exact solutions
- Non-equilibrium steady states (intro)
- Stochastic thermodynamics preview
Notes
Topics reflect common graduate physics core and elective syllabi at US universities. Sequencing and emphasis vary between one- and two-semester treatments.