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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Spectral theory of the Schr?dinger operators on fr
actals - Molchanov\, S (University of North Caroli
na)
DTSTART;TZID=Europe/London:20150625T100000
DTEND;TZID=Europe/London:20150625T110000
UID:TALK59944AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/59944
DESCRIPTION:Spectral theory of the Schr?dinger operators on fr
actals (Stanislav Molchanov UNC Charlotte) \n\nSpe
ctral properties of the Laplacian on the fractals
as well as related topics (random walks on the fra
ctal lattices\, Brownian motion on the Sierpinski
gasket etc.) are well understood. The next natural
step is the analysis of the corresponding Schr?di
nger operators and not only with random ergodic po
tentials (Anderson type Hamiltonians) but also wit
h the classical potentials: fast decreasing\, incr
easing or periodic (in an appropriate sense) ones.
The talk will present several results in this dir
ection. They include a) Simon Spencer type theore
m (on the absence of a.c. spectrum) and localizati
on theorem for the fractal nested lattices (Sierpi
nski lattice) b) Homogenization theorem for the ra
ndom walks with the periodic intensities of the ju
mps c) Quasi-classical asymptotics and Bargman typ
e estimates for the Schr?dinger operator with the
decreasing gasket d) Bohr asymptotic formula in th
e case of the increasing to infinity potentials e)
Random hierarchical operators\, density of states
and the non-Poissonian spectral statistics Some p
arts of the talk are based on joint research with
my collaborators (Yu. Godin\, A. Gordon\, E. Ray\,
L. Zheng).\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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