Statistical mechanics
Master PhysiqueParcours Cell Physics
Description
The aim of this course is to use the statistical physics tools developed in L3 to describe complex systems in modern physics, such as quantum ideal gases (Bose-Einstein condensation, for example) and interacting systems (Ising model, liquid-gas transition, electrolyte, etc.).
Compétences requises
Have taken a basic course in equilibrium statistical physics. Knowledge of and ability to manipulate the formalism of microcanonical and canonical sets for systems without interactions (e.g. perfect gas, paramagnetism, etc.).
Compétences visées
Applying knowledge in physics;
Apply methods from mathematics and digital technology;
Produce a critical analysis, with hindsight and perspective;
Research a current physics topic using specialised resources;
Communicate in writing and orally, including in English.
Syllabus
I-Perfect quantum gases
I.1 Perfect Fermions gases: high-temperature limit, degenerate Fermi gas, low temperature development of Sommerfeld, classical limit;
I.2 Perfect Bosons gases: high-temperature limit, Bose-Einstein condensation, black-body radiation.
II-Systems in interactions and phase transitions: the Ising model
II.1 Introduction to the Ising model: definition and general relations, mean field theory, critical exponents.
II.2 Exact solutions at 1d and 2d;
II.3 Correlation function in the mean field approximation;
II.4 Landau theory.
III-Classical fluids
III.1 Classical fluids, multi-point correlation functions, pair correlation function;
III.2 Viriel development;
III.3 Electrolytes and plasmas: Debye-Hückel model.
Bibliographie
- Introduction to Modern Statisticam Mechanics, D. Chandler, Oxford University Press.
- Elements de Physique statistique, B. Diu, C. Guthmann, D. Lederer, B. Roulet, Hermann.
- Statistical Mechanics, Shang-Keng Ma, World Scientific.
- Equilibrium Statistical Physics, M. Plischke and B. Bergersen, World Scientific.
- Des Phénomènes Critiques aux Champs de Jauge, M. Le Bellac, Savoirs Actuels, InterEditions/Editions du CNRS.
- Introduction to Phase Transition and Critical Phenomena, H. Stanley, Oxford Sci. Publications.
- The Theory of Critical Phenomena: an Introduction to the Renormalization Group, J. J. Binney, N. J. Dowrick, A. J. Fisher and M. E. J. Newman, Oxford Science Publication.