Characterization of the metal-insulator transport transition for the two-particle Anderson model

Abstract

We extend to the two-particle Anderson model the characterization of the metal-insulator transport transition obtained in the one-particle setting by Germinet and Klein. 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 this new version, operators are restricted to boxes defined with respect to the pseudo-distance in which we have the slow spreading. At the bottom of the spectrum, within the regime of one-particle dynamical localization, we show that this modified multiscale analysis yields dynamical localization for the two-particle Anderson model, allowing us to obtain a characterization of the metal-insulator transport transition for the two-particle Anderson model at the bottom of the spectrum.

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• An eigensystem approach to Anderson localization for multi-particle systems