Statistical Physics

Classes and lectures provide a review of some selected topics of statistical physics, along with a discussion of basic mathematical tools such as probability theory, statistics and stochastic processes. A particular attention is payed to the role of statistical physics in thermodynamics of gaseous and magnetic systems and in quantum theory. Some examples of using this method in related sciences (astronomy, biophysics) are also presented.

Lectures

1. Basics of probability theory.

2. Stochastic processes, Markov chains and Langevin equation.

3. Entropy vs. information. States of maximal entropy

4. Description of statistical systems. Evolution and equilibrium states.

Thermodynamic formalisms.

5. Thermodynamics of gas systems:

a) perfect gas

b) nonideal gases (virial expansion, mean field theory)

6. Thermodynamics of magnetic systems:

a) paramagnetics and Curie law

b) Ising model of nearest neighbours

c) phase transition in a Curie-Weis-Kac model

7*. Grand canonical ensemble and theory of phase transitions

8. Quantum Statistical systems:

a) formalism of quantum mechanics

b) multilevel system: Bose-Einstein and Fermi-Dirac statistics

9. Quantum gases

a) electron gas in metal

b) stability of white dwarfs

c) Bose-Einstein condensation

d) photonic gas and thermal radiation

e) phonons and crystals

f) basics of superconductivity

* not obligatory

Exercise: selected topics of statistical physics

- C. J. Thompson, Mathematical Statistical Physics

- R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics

T. C. Dorlas, Statistical Mechanics. Fundamentals and Model Solutions

Written exam + oral discussion

50-60% - grade: 3

60-70% - grade: 3+

70-80% - grade: 4

80-90% - grade: 4+

90-100% - grade 5