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DTSTART:20170326T030000
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DTSTART:20171029T020000
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DTSTAMP:20220817T020935Z
UID:57f791caf1450061091989@ist.ac.at
DTSTART:20170406T160000
DTEND:20170406T180000
DESCRIPTION:Speaker: Mitia Duerinckx\nhosted by Julian Fischer\nAbstract: W
e discuss the long-time transport properties of the SchrÃ¶dinger equation
with a disordered potential of weak intensity. In the periodic setting\, t
he usual Bloch wave decomposition reduces the problem to the perturbation
of a simple isolated eigenvalue\, while in the quasi-periodic case the cor
responding eigenvalue is no longer isolated and while in the random case i
t is even immersed in an absolutely continuous spectrum. Such a perturbati
on analysis in the periodic setting easily leads to asymptotic ballistic t
ransport properties\, but the situation is very different and much more un
clear in the two other situations. And for good reasons: in the random set
ting it is indeed known that the transport rather becomes diffusive on ver
y long timescales. In this talk\, we show how the construction of a trunca
ted perturbation series\, only approximately solving the perturbed eigenva
lue equation\, can be used in the quasi-periodic setting to rigorously pro
ve that ballistic transport holds at least up to exponential times. In the
random setting\, a similar approach allows to optimally determine the cri
tical time up to which ballistic transport holds\, in terms of the decay o
f the correlations of the potential.\n
LOCATION:Seminar room Big Ground floor / Office Bldg West (I21.EG.101)\, IS
TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Mitia Duerinckx: Approximate spectral approach to asymptotic transp
ort properties of quantum waves
URL:https://talks-calendar.app.ist.ac.at/events/404
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