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SUMMARY:Spectral theory of the Schr?dinger operators on fractals - Molchan
 ov\, S (University of North Carolina)
DTSTART:20150625T090000Z
DTEND:20150625T100000Z
UID:TALK59944@talks.cam.ac.uk
CONTACT:42080
DESCRIPTION:Spectral theory of the Schr?dinger operators on fractals (Stan
 islav Molchanov UNC Charlotte) \n\nSpectral properties of the Laplacian on
  the fractals as well as related topics (random walks on the fractal latti
 ces\, Brownian motion on the Sierpinski gasket etc.) are well understood. 
 The next natural step is the analysis of the corresponding Schr?dinger ope
 rators and not only with random ergodic potentials (Anderson type Hamilton
 ians) but also with the classical potentials: fast decreasing\, increasing
  or periodic (in an appropriate sense) ones. The talk will present several
  results in this direction. They include a) Simon  Spencer type theorem (o
 n the absence of a.c. spectrum) and localization theorem for the fractal n
 ested lattices (Sierpinski lattice) b) Homogenization theorem for the rand
 om walks with the periodic intensities of the jumps c) Quasi-classical asy
 mptotics and Bargman type estimates for the Schr?dinger operator with the 
 decreasing gasket d) Bohr asymptotic formula in the case of the increasing
  to infinity potentials e) Random hierarchical operators\, density of stat
 es and the non-Poissonian spectral statistics Some parts of the talk are b
 ased on joint research with my collaborators (Yu. Godin\, A. Gordon\, E. R
 ay\, L. Zheng).\n
LOCATION:Seminar Room 1\, Newton Institute
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