Learning outcomes

This course of theoretical physics deals with the statistical analysis of mechanical systems composed of a huge number of identical particles. The course is a bridge between the mechanics of many body systems and the thermodynamics.
 

Goals

To derive the laws of distribution of energy for quasi-classical particles (Boltzmann law) and quantum particles (Fermi-Dirac and Bose-Einstein distributions). To apply these laws to the kinetics theory of gases (Maxwell distribution and applications), to the vibrations of molecules, to black body radiations, together with perfect gases of bosons and fermions.
 

Content

After having setting out the fundamental principles of statistical mechanics and having made it clear the concept of equilibrium, the laws of distribution of energy are derived on the basis of maximum entropy in the grand canonical framework. From there, the Gibbs distribution for canonical ensembles is easily deduced. Applications are developed for perfect gases of semi-classical and quantum particles and to quasi-particles (phonons and photons). Interactions between particles are finally introduced, in the frame of the virial theorem and the Ising model.
 

Table of contents

Number of microscopic states and entropy for a system of classical and semi-classical particles, principle of maximum entropy, Boltzmann law of distribution, law of distribution of momentum of Maxwell, kinetics theory of gas
Number of microscopic states for non-interacting bosons and fermions, Bose-Einstein and Fermi-Dirac laws of distribution
Black body radiations: Planck's law, concept of photons and thermodynamical properties
Superfluidity of 4He and the perfect gas bosons
Electronic properties of metals and the perfect gas of fermions
The virial theorem
The Ising model
 

Exercices

Resolution of a few illustrative problems by an assistant professor

Assessment method

Oral exam on the theoretical topics covered by the lectures (2/3 of the grade) plus a written test about applications (1/3 of the grade)

Sources, references and any support material

C. Ngô et H. Ngô, Physique statistique : Introduction (Dunod, Paris, 2008).
 
H. Bacry, Introduction aux concepts de la physique statistique (Ellipses Marketing, Paris, 1998)
 
D. J. Amit et Y. Verblin, Statistical Physics: An introductory course (World Scientific, New-York, 1999)
 

Language of instruction

Français
Training Study programme Block Credits Mandatory
Standard 0 3
Standard 3 3