Efficient localization bounds in a continuous multi-particle Anderson model with long-range interaction

TL;DR

This paper proves strong dynamical localization for multi-particle Anderson models with long-range interactions, establishing uniform decay bounds on eigenfunction correlators in continuous space at low energies.

Contribution

It introduces the first proof of uniform decay bounds on eigenfunction correlators in multi-particle continuous models with infinite-range interactions.

Findings

Proves strong dynamical localization in the specified model.

Establishes uniform decay bounds on eigenfunction correlators.

Addresses localization in the norm-distance metric.

Abstract

We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the mathematical literature, the uniform decay bounds on the eigenfunction correlators at low energies are proved, in the multi-particle continuous configuration space, in the norm-distance and not in the Hausdorff pseudo-metric.