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TZID:Europe/Paris
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BEGIN:VEVENT
UID:1-95@lptms.universite-paris-saclay.fr
DTSTART:20130319T110000Z
DTEND:20130319T120000Z
DTSTAMP:20130315T113950Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
s-g-biroli/
SUMMARY:Séminaire du LPTMS: G. Biroli - LPTMS\, salle 201\, 2ème étage\,
Bât 100\, Campus d'Orsay - 19 Mar 13 11:00
DESCRIPTION:Difference between Ergodicity\, Level Statistics and Localizati
on Transitions on the Bethe Lattice\nGiulio Biroli\, IPhT Saclay\nRandom M
atrix Theory was initially developed to explain the eigen-energy distribut
ion of heavy nuclei. It has become clear by now that its domain of applica
tion is much broader and extends to very different fields such as number t
heory and quantum chaos\, just to cite a few. In particular\, it has been
conjectured---and proved or verified in some special cases---that quantum
ergodic (or chaotic) systems are characterized by eigen-energies statistic
s in the same universality class of random matrices and by eigen-functions
that are delocalized over the configuration space. On the contrary\, non-
ergodic quantum systems\, such as integrable models\, are expected to disp
lay a Poisson statistics of energy levels and localized wave-functions. St
arting from Anderson's pioneering papers\, similar properties have also be
en studied for electrons hopping in a disordered environment. Remarkably\,
also in this case\, similar features of the energy-level statistics have
been found. All that has lead to the conjecture that delocalization in con
figuration space\, ergodicity and level statistics are intertwined propert
ies. \nIn this talk we revisit the old problem of non-interacting electro
ns hopping on a Bethe lattice with on-site disorder. By using numerical si
mulations\, the cavity method and mapping to directed polymers in random m
edia we unveil the existence of an intermediate phase in which wave-functi
ons are delocalized but the energy-level statistics is Poisson. This new p
hase\, in which the system is non-ergodic but delocalized\, may play an im
portant role in several fields from random matrix theory to strongly inter
acting quantum disordered systems\, in particular it could be related to t
he non-ergodic metallic phase conjectured to exist in the context of Many-
Body Localization.
LOCATION:LPTMS\, salle 201\, 2ème étage\, Bât 100\, Campus d'Orsay\, 15
Rue Georges Clemenceau\, Orsay\, 91405\, France
GEO:48.698185;2.181768
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=15 Rue Georges Clemenceau\,
Orsay\, 91405\, France;X-APPLE-RADIUS=100;X-TITLE=LPTMS\, salle 201\, 2è
me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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