Statut Confirmé Série COURS Domaines physics Date Vendredi 16 Mars 2012 Heure 10:00 Institut IPHT Salle Salle Claude Itzykson, Bât. 774, Orme des Merisiers Nom de l'orateur Konstantin B. Efetov Prenom de l'orateur Addresse email de l'orateur Institution de l'orateur Ruhr-Universität Bochum et IPhT Titre Supersymmetry in Condensed Matter and Statistical Physics (2/5) Résumé The goal of these lectures is to present an introduction to the use of modern, Supersymmetryinspired tools in Condensed Matter and in Statistical Physics. \par I will motivate why Grasmann variables are useful in the study of disordered metals. I will show how one develops the conventional diagrammatic technique, and why one encounters problems in applying it for most interesting systems. Then, I will show how anti-commuting variables help averaging over the disorder, and I will derive the super-matrix non-linear $\sigma$-model. After that I will present how non-trivial problems of disordered systems have been attacked by using the $\sigma$-model. Proceeding in this way I will discuss Anderson localization in one dimensional thick wires and in two dimensional films, and I will find the solution in high dimensionality or on the Bethe lattice. Then, I will present how the zero dimensional $\sigma$-model can be useful for mesoscopic systems, and I will show that Random Matrix Theory is equivalent to the zero dimensional $\sigma$-model. This equivalence establishes the connection between disordered mesoscopic systems and quantum chaos. I will show an extension of the conventional $\sigma$-model to the ballistic one and an exact mapping onto a generalized $\sigma$-model (super-bosonization formula). The tentative plan of the lectures follows. \\ \\ 1 - Disorder in normal metals. \\ 2 - Grassmann variables and non-linear supermatrix $\sigma$-model. \\ 3 - Renormalization group for the $\sigma$-model in 2 and 2 + $\varepsilon$ dimensions. \\ 4 - Solving one dimensional and high dimensional models. \\ 5 - Zero dimensional $\sigma$-model for small metal particles. Random Matrix Theory and the supersymmetry. Ballistic $\sigma$-model and Superbosonization. Numéro de preprint arXiv Commentaires Cours organisés en collaboration avec l'Ecole Doctorale de Physique de la Région Parisienne - ED 107. Fichiers attachés Affiche_Efetov_2012-02-13.pdf (133341 bytes)

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