The  Weizmann  Institute  of  Science
                  Faculty of Mathematics and Computer Science
 
                 Mathematical Analysis and Applications Seminar
 
                     Lecture Hall, Room 1, Ziskind Building
                           on Tuesday, June 21, 2011
                                  11:00 - noon
 
                                Michael Aizenman
                              Princeton University
 
                                 will speak on
 
               Resonant delocalization for Schrodinger operators
                      with random potential on tree graphs
 
Abstract:
We resolve an existing question concerning the location of the mobility edge
for operators with a hopping term and a random potential on the Bethe lattice.
For  unbounded potential we find that extended states appear  well beyond the
spectrum of the operator's hopping term, including in a  Lifshitz tail regime
of very low density of states.  The relevant mechanism is the formation of
extended states through disorder enabled resonances, for which the exponential
increase of the volume plays an essential role.  This mechanism has also the
surprising implication that for bounded random potentials at weak disorder
there is no mobility edge in the form that was envisioned before.  (Joint work
with Simone Warzel.)
 
            Mathematical Analysis and Applications Seminar Web Page:
               <http://www.wisdom.weizmann.ac.il/~vered/analsem.html>
 
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Diana Mandelik   <diana.mandelik@weizmann.ac.il>