Pantheon SEMPARIS Le serveur des séminaires parisiens Paris

Statut Confirmé
Série LPTMS
Domaines physics
Date Mardi 8 Janvier 2019
Heure 11:00
Institut LPTMS
Salle LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
Nom de l'orateur Franchini
Prenom de l'orateur Fabio
Addresse email de l'orateur
Institution de l'orateur Institut Ruder Boškovic, Zagreb, Croatia
Titre Spontaneous Ergodicity Breaking in Invariant Matrix Models
Résumé We reconsider the study of the eigenvectors of a random matrix, to better understand the relation between localization and eigenvalue statistics. Traditionally, the requirement of base invariance has lead to the conclusion that invariant models describe only extended (conductive) systems. We show that deviations of the eigenvalue statistics from the Wigner-Dyson universality reflects itself on the eigenvector distribution. In particular, gaps in the eigenvalue density spontaneously break the U(N) symmetry to a smaller one, hence rendering the system not anymore ergodic. Models with log-normal weights, recently considered also in string theory models such as ABJM theories, show a critical eigenvalue distribution which would indicate a critical breaking of the U(N) symmetry, supposedly resulting into a multi-fractal eigenvector statistics. These results pave the way to the exploration of localization problems using random matrices via the study of new classes of observables and potentially to novel, interdisciplinary, applications of matrix models.
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