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BEGIN:VEVENT
UID:0-643@lptms.universite-paris-saclay.fr
DTSTART:20190115T110000Z
DTEND:20190115T120000Z
DTSTAMP:20181204T143924Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
s-fabio-franchini/
SUMMARY:Séminaire du LPTMS: Fabio Franchini - LPTMS\, salle 201\, 2ème é
tage\, Bât 100\, Campus d'Orsay - 15 Jan 19 11:00
DESCRIPTION:Spontaneous Ergodicity Breaking in Invariant Matrix Models\nFab
io Franchini (Institut Ruđer Bošković\, Zagreb\, Croatia)\nWe reconside
r 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 inva
riant models describe only extended (conductive) systems. We show that dev
iations of the eigenvalue statistics from the Wigner-Dyson universality re
flects 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 th
eories\, show a critical eigenvalue distribution which would indicate a cr
itical breaking of the U(N) symmetry\, supposedly resulting into a multi-f
ractal eigenvector statistics. These results pave the way to the explorati
on of localization problems using random matrices via the study of new cla
sses of observables and potentially to novel\, interdisciplinary\, applica
tions of matrix models.
CATEGORIES:seminars
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15
Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
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Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
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