Statistical Physics B (advanced) 1102-4AF12

The lecture consists of two unequal parts. The first, shorter part (appr. 8 hours) is devoted to phenomenological thermodynamics of equilibrium states. The neo-Gibbsian approach to thermodynamics is presented, but relation to the classical formulations by Clausius, Kelvin and Caratheodory of the Second Law are also discussed. After introducing the thermodynamic potentials ( via the Legendre transform) and their extremum principles , the thermodynamic theory of phase transitions and critical phenomena (together with the concept of critical indices) is introduced.
The second, part is devoted to the classical and quantum statistical mechanics of equilibrium states. The theory of statistical ensembles: microcanonical, canonical and grand canonical is presented. The application of statistical mechanical methods to ideal and real gases and magnets is presented. In particular the Ising model is introduced and the Debye-Hueckel theory is presented. The theory of Gibbs statistical ensembles is presented based on the equal probabilities postulate, from which probability distribution functions for canonical and grand canonical ensembles are derived.
On the quantum level the theory of ideal Fermi and Bose gases is presented with applications to the black body radiation, Bose-Einstein condensation, and the theory of specific heat of crystals, containing both the electron and phonon contributions.

Type of course

obligatory courses

Mode

Classroom

Prerequisites (description)

The purpose of this lecture is to present the fundamentals of phenomenological thermodynamics of equilibrium states (the neo-Gibbsian approach) and the fundamentals of statistical mechanics, both classical and quantum. Home assignements form the essential part of this lecture. Each week a set of 3-5 problems is provided to the students, and one of the problems is picked next week to check the solution and mark it. The, if necessary, the most common mistakes and problems with the correct solution, are discussed the next week. The points obtained in this way contribute to the overall evaluation of students.

Learning outcomes

This lecture aims at forming the students ability to derive the macroscopic properties of macroscopic systems on the basis of their microscopoic structure and interactions. An emphasis is put on constructing the models as well as approximate procedures to realize the above purpose.

Assessment criteria

The students can collect points on the basis of two colloquia (2x15 points) and home assignments (15 points). The minimum which makes the student eligible to start the exam is 22 points. The exam consists of two parts: written and oral. The final mark is based on the results of wriiten exam, oral exam and the number of points collected during the classes.

Bibliography

1. L. Landau, E. Lifschitz, Statistical Physics
2. H. Callen, Thermodynamics and an Introduction to Thermostatistics
3. M. Kardar, Statistical Physics of Particles
4. K. Huang, Statistical Mechanics
5. R. Pathria, Statistical Mechanics

Additional information

Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1102-4AF12 in USOSweb