Insights from Statistical Mechanics on the Spectra and Dynamics of Operators with Disorder
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Ever since the Wigner-Dyson ensembles of random matrices and the
Anderson model of random Schroedinger operators, lessons from
statistical mechanics have led to fundamental insights into the
effects of disorder on spectra and dynamics of random operators,
and indeed also on the effects of pseudo-randomness which reach as
far afield as number theory. The talk will focus on some recent
developments in the mathematical studies of localization and
related gap statistics. One may note there again the long reach of
some of the central themes of modern statistical mechanics - which
of course need to be combined with mathematical tools which are
specific to the subject. (Included in the discussion is recent
joint work with S. Warzel.)