Efficient Localization Bounds in a Continuous N-Particle Anderson Model with Long-Range Interaction

We establish strong dynamical and exponential spectral 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 (EFCs) at low energies are proved, in the multi-particle continuous configuration space, in the (symmetrized) norm-distance, which is a natural distance in the multi-particle configuration space, and not in the Hausdorff distance. This results in uniform bounds on the EFCs in arbitrarily large but bounded domains in the physical configuration space, and not only in the actually infinite space, as in prior works on multi-particle localization in Euclidean spaces.