STATISTICAL PHYSICS
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- GIUSEPPE PAGLIARA
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- FIS/04
Training objectives
- The course is basically an introduction to statistical physics with the aim of presenting the main concepts and to provide the most important mathematical tools for dealing with macroscopic systems. From classical statistical physics to quantum statistical physics, from equilibiurm physics to elements of non-equilibrium physics and transport phenomena, the course will touch also applications to modern research topics. At the end the student will be able to analyze multi-particle systems in presence of interaction, to pin down the most important degrees of freedom and to qualitatively describe the possible phases.
Prerequisites
- A good knowledge of classical and quantum physics at the level of undergraduate is needed together with a good knowledge of the mathematical methods of physics (calculus, geometry, analytic functions , Hilbert spaces). It is also useful if the students have attended the lectures of atomic and solid state physics although many aspects (such as the quantum statistics) will be anyway treated in a more general context.
Course programme
- The course is organized in five chapters:
1) Reminder of thermodynamics, thermodynamical potentials, phenomenological description of first order phase transitions (Maxwell construction, Gibbs phase rule), 12 h.
2) The statistical approach, Boltzmann and Gibbs entropy, systems of independent and localized particles, 4 h. Non equilibrium physics, Boltzmann equation and H-theorem, 4h.
3) Classical ensembles (microcanonical, canonical, grancanonical), partition functions, fluctuation-dissipation relations. Virial expansion for interacting particles, 12 h.
4) Density matrix and quantum statistical ensembles, quantum statistics and applications (BEC, Landau diamagnetism*) 10 h.
5) Theory of phase transitions (1D Ising model, 2D Ising model in mean field approximation, Ginzburg Landau theory*). Critical exponents, 12 h.
*: only for students of a.a. 2019-20 Didactic methods
- Being a theoretical course, most of the lectures will be presented at the black board. Slides will be also used for showing complicated plots (such as phase diagrams) and a few examples of numerical computations will be shown by using the software Mathematica. Roughly one third of the course will be dedicated to exercises and to examples for which analitical calculations are feasible (the partition functions of some specific physical systems).
Learning assessment procedures
- The exam consists in a written exam and a oral exam. The written one aims at evaluating the skills of the students in using the mathematical tools of statistical mechanics (thermodynamical potentials, partition functions, equations of state, heat capacities, fluctuations-dissipations relations). The duration is of two hours, the student can use a sheet of usefull formulae. A minimum of 16/30 is needed to pass the written exam. The oral exam aims at evaluating if the students have learnt the main concepts of statisical mechanics in the context of thermodynamics, ensemble theories, phenomenology of phase transitions.
Reference texts
- The lectures are mainly based on:
"Statistical Mechanics" di R.K. Pathria & P.D. Beale.
Usefull references are also the following books:
"Elementary Statistical Physics" di C. Kittel
"Thermal Physics" di C. Kittel
"Statistical mechanics" di K. Huang
"Statistical physics" di L.D. Landau & E.M. Lifshitz
