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Exponential dynamical localization in N-particle Anderson models on graphs with long-range interaction via Fractional Moment Analysis

Wednesday 18th February 2015 - 14:00 to 15:00
INI Seminar Room 2
In this talk, we extend the techniques of the multi-particle variant of the Fractional Moment Method,developed by Aizenman and Warzel, to disordered quantum systems in general finite or countable graphs with polynomial growth of balls, in presence of an exponentially decaying interaction of infnite range. In the strong disorder regime, we prove complete exponential multi-particle strong dynamical localization. Prior results, obtained with the help of the multi-scale analysis, proved only a sub-exponential decay of eigenfunction correlators for such systems.

We also comment on recent results on exponential spectrallocalization in presence of a slower (sub-exponentially) decaying interaction,in discrete and continuous models.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons