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SUMMARY:Kirk Distinguished Visiting Fellow Lecture: The hidden landscape o
 f localization - Svitlana Mayboroda  (University of Minnesota)
DTSTART:20190612T150000Z
DTEND:20190612T160000Z
UID:TALK125905@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Complexity of the geometry\, randomness of the potential\, and
  many other irregularities of the system can cause powerful\, albeit quite
  different\, manifestations of localization: a phenomenon of confinement o
 f waves\, or eigenfunctions\, to a small portion of the original domain. I
 n the present talk we show that behind a possibly disordered system there 
 exists a clear structure\, referred to as a landscape function\, which pre
 dicts the location and shape of the localized eigenfunctions\, a pattern o
 f their exponential decay\, and delivers accurate bounds for the correspon
 ding eigenvalues in the range where\, for instance\, the classical Weyl la
 w notoriously fails. We will discuss main features of this structure unive
 rsally relevant for all elliptic operators\, as well as specific applicati
 ons to the Schrodinger operator with random potential and to the Poisson-S
 chrodinger drift-diffusion system governing carrier distribution and trans
 port in semiconductor alloys.   <br><br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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