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

TL;DR

This paper extends the characterization of the metal-insulator transition from one-particle to two-particle Anderson models, demonstrating that slow wave packet spreading implies dynamical localization at the spectrum's bottom.

Contribution

It introduces a modified bootstrap multiscale analysis tailored for the two-particle Anderson model, enabling the characterization of the metal-insulator transition.

Findings

Dynamical localization is established for the two-particle model at the spectrum's bottom.

The analysis connects slow wave packet spreading with localization properties.

A new multiscale analysis framework is developed for multi-particle systems.

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.