| Abstract: | Of current research interest in the area concerning the disorder effects on the dynamics under random Schroedinger operators is the occurrence of energy regimes (phases) in which extended states are formed from resonating local quasi-modes. The corresponding eigenstates are ``non-ergodic'', in the sense that they violate a heuristic version of the equidistribution principle, yet they do not exhibit Anderson localization. Such phases were proven to occur in the the random Schroedinger operator on tree graphs (in a joint work with Simone Warzel), and are also expected to show up in many-particle systems which are the subject of ongoing work (with SW and Mira Shamis). |
