Statistical Physics (PHYS552)


Course Materials: Syllabus

Course textbook:

M. LeBellac, F. Mortessagne, G.G. Batrouni, Equilibrium and Non-Equilibrium Statistical Thermodynamics, Cambridge University Press (2006)



Lecture Notes:

Lecture 1: Thermodynamics (Laws of thermo, Carnot cycle, entropy)

Lecture 1: Thermodynamics (work vs. heat, thermodynamics walls, equilibrium state)

Lecture 2: Thermodynamics (entropy, constraints, internal variables, heat engines)

Lecture 2: Thermodynamics (postulating entropy, internal constraints, intensive variables, heat engine again, thermodynamic potentials)

Lecture 3: Thermodynamics (Legendre transforms, Massieu functions, specific heats/response functions, stability, 3rd law revisited)

Lecture 4: Probabilistic description of quantum mechanics (time-dependent Schroedinger equation, Schroedinger vs. Heisenberg pictures, density matrix)

Lecture 4: Probabilistic description of classical mechanics (phase space, phase space density, Liouville theorem, ergodicity)

Lecture 5: Statistical entropy, tensor products, density matrices associated with a quantum statistical mixture

Lecture 5: Equilibrium distribution, ensembles, fluctuation response

Lecture 6: Thermodynamics from the information entropy, entropy of mixing

Lecture 6: Mixing, microscopic reversibility vs. macroscopic irreversibility, increase of entropy, loss of information

Lecture 7: Canonical Ensemble: Application to the ideal gas

Lecture 7: Microcanonical and Canonical Ensembles: Application to paramagnets and the 1D Ising model

Lecture 8: Thermodynamic limit, Classical systems, Maxwell distribution

Lecture 8: Equipartition theorem, Ideal gas of diatomic molecules (classical and quantum), Virial theorem

Lecture 9: Quantum statistical mechanics: canonical ensemble in the path-integral representation

Lecture 10: Liquids, pair distribution function, virial expression for pressure

Lecture 10: Chemical potential, phase equilibria, Gibbs phase rule

Lecture 11: Equilibrium at constant pressure, van der Waals equation of state, equal area construction

Lecture 11: Equilibrium at constant chemical potential, associated equal area construction

Lecture 12: Chemical reactions, grand canonical ensemble (brief intro)

Lecture 13: Critical phenomena, Ising model (D=1, D=2, Peierls argument), Lee-Yang theorem

Lecture 13: Correlation functions, Correlation length of Ising model in 1D, Symmetry breaking

Lecture 14: Critical exponents (definition), basic mean-field theory

Lecture 14: General approximation theory, mean-field theory, critical exponents from mean-field theory

Lecture 15: Ginzburg-Landau theory (basic), Ginzburg-Landau functional from coarse-graining, critical exponents, correlation functions

Lecture 15: Goldstone modes, Ginzburg-Landau functional, second-order expansion, critical dimension

Lecture 16: Homogeneous functions, Widom scaling, Kadanoff scaling

Lecture 16: Basics of renormalization group theory

Lecture 17: Renormalization group example: triangular lattice

Lecture 17: Renormalization group in more detail: scaling transformations

Lecture 18: Critical manifolds, fixed points, limiting distributions, correlation functions, magnetization and free energy

Extra Lecture Notes:

Lecture 19: Ideal quantum gases, Ideal Bose gas

Lecture 19: Bose-Einstein condensation, Ideal Fermi-Dirac gas

Exams:

Hour Exam 1 (Solutions)

Hour Exam 2 (Solutions)

Hour Exam 3 (Solutions)

Hour Exam 4 (Solutions)

Final Exam (Solutions)