Statistical Physics B

The students entering the course are expected to have completed an introductory course on statistical physics and thermodynamics as well as the standard undergraduate level courses (classical and quantum mechanics, electrodynamics). Some knowledge of fluid mechanics and stochastic processes is useful.

Statistical physics is the branch of physics that describes many-body systems with methods from probability theory and statistics. Fundamentally, it describes a link between the microscopic world governed by, for example, classical or quantum mechanics, and the macroscopic world governed by thermodynamics. Later it was found that general methods of statistical physics can be even applied to other systems, such as financial markets or social networks.

Typically, introductory courses in statistical physics discuss ensemble theory with several applications to ideal systems in equilibrium. In Statistical Physics B, we go a step further by discussing interacting systems and out-of-equilibrium systems.

1. Recap basic statistical mechanics

2. Introduction phase transitions and Ising model in mean-field. Breakdown of mean-field

3. Statistical fields, Hubbard-Stratonovich transformation, continuous symmetries, Goldstone modes. Examples: magnets, nematic liquid crystals, superfluids.

4. Correlation functions (on Gaussian level), Ginzburg criterion, upper and lower critical dimension.

5. BKT transition (qualitative)

6. Classical fluids: density-density correlations, potential of mean force, structure factor, Ornstein-Zernike, hard spheres, charged fluids.

7. Linear irreversible thermodynamics, phenomenological equations, entropy production, Onsager reciprocity

8. Time correlators, linear response theory, Onsager regression hypothesis

9. Spectral analysis of fluctuations, Kramers-Kronig relations, Green-Kubo relations. Application to Brownian motion.

D. Chandler - Introduction ot modern statistical mechanics

R. K. Pathria and P. D. Beale, Statistical Mechanics

K. Huang, Statistical mechanics

F. Schwabl, Statistical mechanics

R.H. Swendsen, An introduction to statistical mechanics and thermodynamics

F. Mandl, Statistical physics

H.B. Callen, Thermodynamics

J. K. G. Dhont – An introduction to the dynamics of colloids

S. R. de Groot and P. Mazur – Non-equilibrium thermodynamics

J.-P. Hansen and I. R. MacDonald - Theory of simple liquids

R. Zwanzig - Nonequilibrium Statistical Mechanics

The student will have a working knowledge of how to apply statistical mechanics in and out of equilibrium.

- Hand-in exercises (5x, 10%), Mid-term exam (written, 30%), Final exam (written, 60%).

- In retake session one can base the grade on just the final exam and the oral exam.

- In order to pass the course it is required to have more than 50% of the attainable points of the final exam.