Learning objectives
<br />The purpose of the course is to provide basic concepts of quantum statistical mechanics of many-body systems.
Prerequisites
Quantum mechanics, quantum statistical mechanics.
Course unit content
<br />Basic statistical mechanics, density matrix, entropy, ensambles, Wigner function. Identical particles, second quantization, phonons, Hubbard model, spin models. Reduced 1- and 2-body density matrices, correlations in free Fermi and Bose gases. Electron gas, Hartree-Fock method, plasma oscillations. Green functions, equations of motion, perturbation theory, Feynman diagrams.<br />Computer simulation : exact solution of Heisenberg and/or Hubbard models on clusters, calculation of correlation functions and of thermodynamic observables.
Bibliography
A: Messiah : Quantum mechanics.<br />A. Fetter and J. Walecka : Quantum theory of many-particle systems.<br />G. D. Mahan : Many-particle physics.<br />G. Rickayzen : Green's functions and condensed matter.<br />D.C. Mattis : The theory of magnetism.