Density of States under non-local interactions III. N-particle Bernoulli--Anderson model

Abstract

Following [7,8], we analyze regularity properties of single-site probability distributions of the random potential and of the Integrated Density of States (IDS) in the Anderson models with infinite-range interactions and arbitrary nontrivial probability distributions of the site potentials. In the present work, we study $2$-particle Anderson Hamiltonians on a lattice and prove spectral and strong dynamical localization at low energies, with exponentially decaying eigenfunctions, for a class of site potentials featuring a power-law decay.

References in corpus (2)

• Multiparticle localization for disordered systems on continuous space via the fractional moment method
• Universality of smoothness of Density of States in arbitrary higher-dimensional disorder under non-local interactions I. From Viéte--Euler identity to Anderson localization