Advanced Quantum Statistical Physics-S3

Advanced Quantum Statistical Physics

Contact: Pr. Thierry Martin

 

The course begins with a summary of thermodynamics and with the formulation of quantum statistical mechanics, defining the different ensembles (microcanonical, canonical and grand canonical), specifying the equivalence between them. Next, the method of second quantized fields is introduced, with several applications of this formalism: 1) an application to quantum transport in nanosystems in the Landauer Buttiker picture; 2) Linear response theory is derived in terms of response functions (time ordered Green's functions, retarded Green's functions, imaginary time Green's functions and the correspondance between them; 3) the microscopic theory of superconductivity is derived in the Bogoliubov framework for inhomogeneous system and the Bardeen Cooper Schrieffer (BCS) framework using the BCS wave functions and spécifying the Bogoliubov Valatin transform. Next, the field theoretical path integral formalism is derived for bosons and fermions (the latter using Grasmmann variables) is presented up to the formulation of thermodynamical quantities in terms of Feynman diagrams. The Ginzburg Landau theory of superconductivity is then presented with applications to the various Josephson effects. An introduction to the renormalization group ends the choice of topics.

 

References:

•Huang, Statistical Mechanics
•Doniach & Sondheimer, Green’s functions for the solid state physicist
•Negele & Orland, Quantum many particle systems Chaikin and Lubensky, Principles of condensed matter physics.
•T. Martin, in «Nanophysics: Coherence and Transport » École d'été de Physique des Houches Session LXXXI H. Bouchiat, S. Gueron, G. Montambaux, J. Dalibard eds
•De Gennes, Superconductivity fo Metals and Alloys
•Abrikosov, Fundamental of the theory of metals