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

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.