Welcome to the course of Statistical Mechanics and Thermodynamics. The course will follow the schedule below, where you can also find the link to the weekly exercises. Most of the exercises are taken from a set of about 200 problems that cover most of the material (the full file here).
The final exam will also be based on these set of problems.
The course will be taught by Olena Gomonay and Jairo Sinova jointly. We will have open office hours from 12:30 - 14:30 on Mondays. We can also arrange other times.
The class and exercise schedule is as follows:
Theoretische Physik 4, Statistische Physik Gomonay, Sinova
Montag 8:00 - 10:00, Lorentz-Raum
Dienstag 12:00 - 14:00, Lorentz-Raum
Übungen zur Theoretischen Physik 4 Gomonay, Sinova mit Ass.
Mittwoch 12:00 - 14:00, Galilei-Raum
Donnerstag 12:00 - 14:00, Seminarraum A
Donnerstag 14:00 - 16:00, Seminarraum D
The literature that we will follow is
[1] R. K. Pathrida and Paul D. Beale, Statistical Mechanics, Third Edition.
[2] K. Huang, Statistical Mechanics (Wiley, New York, 1987)
| 1 | Mo, 16. Apr. 2018 08:00 |
Introduction Concepts and definitions in thermodynamics: thermodynamic variables, state functions, quasi-static processes, etc. Reversible and irreversible processes and examples. Exercise for Week 1 |
Gomonay Sinova [2] 1.1 |
| 2 | Di, 17. Apr. 2018 12:00 |
Principles: General principles of thermodynamic and its laws. Introduction of the different thermodynamic potentials. |
Gomonay Sinova [2] 1.2-1.7 |
| 3 | Mo, 23. Apr. 2018 08:00 |
Principles: Maxwell relations and Examples Exercise for Week 2 (22.04.2018) |
Sinova [2] 1.6 |
| 4 | Di, 24. Apr. 2018 12:00 |
Thermodynamic potentials as generation functions: calculation of different thermodynamic variables (P,V from the 1st derivatives, heat capacity as a 2nd derivative). |
Sinova |
| 5 | Mo, 30. Apr. 2018
08:00 |
Phase space and dynamics of the classical multi-body system: Probability function, Liouville’s theorem, Ensemble theory, brief introduction of the different ensembles: microcanonical, canonical, grand canonical. Exercise for Week 3 |
Gomonay Sinova [1] 1.1-1.4, 2.1-2.4[2] 6.1, 6.2 |
| 6 | Mo, 7. Mai 2018 08:00 |
The canonical (Gibbs’) ensemble. the Gibbs’ postulate for the distribution function, the partition function, relation with the thermodynamic potentials Exercise for Week 4 |
Gomonay Sinova [1] 3.1-3.5 [2] 7.1 |
| 7 | Di, 8. Mai 2018 12:00 |
Equation of state of the ideal gas (step-by-step derivation) for the canonical ensemble. Boltzmann and Maxwell distribution. | Gomonay [1] 3.7-3.9, 16.3.A |
| 8 | Mo, 14. Mai 2018
08:00 |
The grand canonical ensemble Consistency of the postulates for the different ensembles Exercise for Week 5 |
Gomonay Sinova [1] 4.1-4.5, 3.6 [2] 7.3, 7.6 |
| 9 | Di, 15. Mai 2018 12:00 |
Quantum systems: Density matrix vs distribution function. Quantum canonical and grand canonical ensemble. | Gomonay Sinova [1] 5.1-5.5 [2] 8.1, 8.2 |
| 10 | Di, 22. Mai 2018 12:00 |
Examples: Ideal gas of the harmonic oscillator (3.8), Discrete level distribution function (black body 7.3); Paramagnets (3.9); Negative temperatures for the systems with finite degrees of freedom. | Gomonay Sinova [1] 3.8-3.10 (7.3) |
| 11 | Mo, 28. Mai 2018 08:00 |
Fermi- and Bose statistics. Indiscernibility of the quantum particles. Symmetry and anti-symmetry of wave functions. Fermi and Bose statistics. Fermi-Dirac and Bose-Einstein distributions for an ideal gas: derivation using the grand canonical ensemble. | Gomonay Sinova [1] 5.4,6.1,6.2,6.3 [2] A.1, A.2, 8.5,8.6 |
| 12 | Di, 29. Mai 2018 12:00 |
(continuation) Fermi-Dirac and Bose-Einstein distributions for an ideal gas: derivation using the grand canonical ensemble. | Gomonay [1] 5.4,6.1,6.2,6.3 [2] A.1, A.2, 8.5,8.6 |
| 13 | Mo, 4. Jun. 2018 08:00 |
Fermi-gas: Equation of state for electron gas in metals and magnetism* of ideal Fermi gas | Sinova [1] 8.1,8.3,8.2* [2] 11.1,11.3* |
| 14 | Di, 5. Jun. 2018 12:00 |
Bose-gas: Equation of state of the photon gas (black body problem). Black-body catastrophe. | Sinova [1] 7.1,7.3 [2] 12.1-12.3 |
| 15 | Mo, 11. Jun. 2018
08:00 |
Bose-gas: (cont) Equation of state of the phonon gas in solids (two limiting cases of low and high temperatures). Bose-Einstein condensation Exercises for Week 9 |
Gomonay Sinova [1] 7.1,7.4,7.2 [2] 12.1-12. |
| 16 | Di, 12. Jun. 2018 12:00 |
Non-ideal gas and Interacting systems: Equation of state of the non-ideal gas (cluster expansion and Virial expansion – van der Walls) Role of correlations, hints for derivation. |
Gomonay Sinova [1] 10.1-10.3,10.7 |
| 17 | Mo, 18. Jun. 2018 08:00 |
Fluctuation theory Fluctuations and concept of local equilibrium.Exercises for Week 10 |
Gomonay [1] 15.1 |
| 18 | Di, 19. Jun. 2018 12:00 |
Thermodynamics of Phase Transitions Definition of phases and phase transition. Phase Equilibrium and the Clausius-Clapeyron relation. Classification of the phase transitions (Erenfest). |
Gomonay [1] 4.6, 4.7 [2] 2.1, 2.2 |
| 19 | Mo, 25. Jun. 2018 08:00 |
Phase transitions Liquid-gas (based on van-der-Waals equation).Exercises for Week 11 |
Gomonay Sinova [1] 12.1, 12.2 [2] 17.5, 17.6 |
| 20 | Di, 26. Jun. 2018 12:00 |
Landau theory of phase transitions. | Gomonay Sinova [1] 12.7, 12.9,12.10 [2] 13.4, 17.1-17.3 |
| 21 | Mo, 2. Jul. 2018 08:00 |
The scaling approach to phase transitions (Kadanoff hypothesis, etc.) | Gomonay Sinova [2] Chapter 18 [1] 12.10, 12.11, 12.12 |