BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Random nonmonotonic multichannel Schr"\;{o}din
ger operators\n\n - Mavi\, R (University of Virgin
ia)
DTSTART;TZID=Europe/London:20150409T150000
DTEND;TZID=Europe/London:20150409T152500
UID:TALK58834AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/58834
DESCRIPTION:Co-author: John Imbrie (University of Virginia) \n
\nAnderson localization is by now well understood
for the standard random Schrodinger operator. On t
he other hand the motivation for the problem\, whi
ch lies in many body systems still lacks a develop
ed theory. For our part we consider several aspect
s arising in more-than-one body systems which prev
ent an immediate application of the methods of one
body systems. In systems such as random Ising mod
els\, energy levels of the system may depend analy
tically on (finite truncations of) random paramete
rs. Of course in the standard Anderson model the d
ependence of the energy levels on the random param
eters is linear which leads to the celebrated Wegn
er estimate which allows the usual multiscale anal
ysis. In our talk\, we consider a single body mod
el with potentials depending analytically on the r
andom parameters. In multichannel Schrodinger mod
els\, the potentials at each site of the lattice a
re matrices which may depend analytically on the r
andom parameters\, eg\, these models can be realiz
ed as tight binding models in $Z^D$ with dilute ra
ndomness. In the multichannel model\, we utilize
the transversality of the system's energies with r
espect to the random environment\, this allows som
e control of the probabilities of resonances. Fina
lly\, we discuss new methods of localization proof
s\, for the multichannel model we obtain stretched
exponential localization of eigenfunction correla
tions.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
END:VEVENT
END:VCALENDAR