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UID:1-30@lptms.universite-paris-saclay.fr
DTSTART:20120315T140000Z
DTEND:20120315T140000Z
DTSTAMP:20120302T130416Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-commun-
lpt-lptms-gregory-berkolaiko/
SUMMARY:Séminaire commun LPT-LPTMS : Gregory Berkolaiko - LPTMS\, salle 20
1\, 2ème étage\, Bât 100\, Campus d'Orsay - 15 Mar 12 14:00
DESCRIPTION:Universality in chaotic quantum transport : the concordance bet
ween random matrix and semiclassical theories\nGregory Berkolaiko\, Texas
A&\;M University\nElectronic transport through chaotic quantum dots exh
ibits universal\, system independent properties which are consistent with
random matrix theory. The observable quantities can be expressed\, via the
semiclassical approximation\, as sums over the classical scattering traje
ctories. Correlations between such trajectories are organized diagrammatic
ally and have been shown to yield universal answers for some observables.\
nWe develop a general combinatorial treatment of the semiclassical diagram
s by casting them as unicellular maps (graphs embedded on surfaces) and re
lating them to factorizations of permutations. The expansion of transport
quantities in inverse channel number corresponds to a genus expansion of t
he combinatorial generating function. Taking previously calculated answers
(Heusler et al\, 2006) for the contribution of a given diagram\, we prove
agreement between the semiclassical and random matrix approaches to momen
ts of the transmission amplitudes. The proof covers all orders\, all momen
ts (including nonlinear)\, and systems with or without time reversal symme
try. It explains the mathematics behind the applicability of random matrix
theory to chaotic quantum transport. The streamlined calculation could al
so pave the way for inclusion of non-universal effects.\nBased on joint wo
rk with Jack Kuipers (Regensburg)
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
me étage\, Bât 100\, Campus d'Orsay:geo:48.698185,2.181768
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