Theoretical / proof-based
Statistical mechanics · Undergraduate · Physics
Topics
Rigorous statistical foundations
- Liouville's theorem and ergodic hypothesis
- Density matrices for statistical ensembles
- Grand partition function as generating function
- Cumulant expansion and linked cluster theorem (sketch)
- Lee–Yang circle theorem context (optional)
Quantum statistics formalism
- Fock space and occupation number representation
- Bose–Einstein condensation mathematics
- Fermi surface and Sommerfeld expansion
- Second quantization for ideal quantum gases
- Kubo formulas for linear response (intro)
Critical phenomena theory
- Landau theory of phase transitions
- Correlation functions and susceptibilities
- Scaling hypotheses and universality
- Renormalization group fixed points (overview)
- Exact solutions: 1D Ising transfer matrix
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$60.00 · 60 min · Undergraduate · Online ($60/hr)
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