Statistical Mechanics of Particles and Fields 1100-SMPF

https://users.fuw.edu.pl/~jeverts/teaching/smopaf/

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.

Koordynatorzy przedmiotu

Jeffrey Everts

Założenia (opisowo)

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.

Efekty uczenia się

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

Kryteria oceniania

To pass the course, students must (i) pass the final exam, and (ii) obtain at least half of the total available points, which determine the final grade. Here the course points are based on hand-in exercises (10%), the midterm exam (40%), and the final exam (50%). In the retake session, requirement (ii) may instead be based entirely on the final exam if this is more favourable to the student.

Literatura

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