Constanza Rojas-Molina

In dimensions higher than two it is expected that a disordered quantum system undergoes a metal-insulator transition from a region of localization to delocalization. For the one-particle Anderson model, F. Germinet and A. Klein showed that the transport exponent in these regions can be related to the applicability of the multiscale analysis method used in the proof of localization. In this talk we present a recent generalization of this characterization to the two-particle Anderson model with short-range interactions. We show that, for any fixed number of particles, the slow spreading of wave packets in time implies the initial estimate of a modified version of the Bootstrap Multiscale Analysis. In the case of two particles, this gives the desired characterization of the metal-insulator transport transition.

This is joint work with A. Klein and S. T. Nguyen.