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SUMMARY:Spectral Properties of Schroedinger Operator with a Quasi-periodic
  Potential in Dimension Two - Karpeshina\, Y (University of Alabama at Bir
 mingham)
DTSTART:20150408T123000Z
DTEND:20150408T133000Z
UID:TALK58817@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-author: Roman Shterenberg (UAB) \n\nWe consider  $H=-Delta+
 V(x)$ in dimension two\, $V(x)$ being a quasi-periodic potential. We prove
  that the spectrum of $H$ contains a semiaxis (Bethe-Sommerfeld conjecture
 ) and that there is a family of generalized eigenfunctions at every point 
 of this semiaxis with the following properties. First\, the eigenfunctions
  are close to plane waves $e^{ilangle ec k\,ec x\nangle }$ at the high e
 nergy region.  Second\, the isoenergetic curves in the space of momenta $
 ec k$ corresponding to these eigenfunctions have a form of slightly distor
 ted circles with holes (Cantor type structure).  It is shown that the spec
 trum corresponding to these eigenfunctions is absolutely continuous. A  me
 thod of multiscale analysis in the momentum space is developed to prove th
 e results.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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