TOWARDS LOCALIZATION IN LONG-RANGE CONTINUOUS INTERACTIVE ANDERSON MODELS

This paper is a follow-up of [8]. The main novelty is the proof of spectral and dynamical localization for a class of interactive Anderson models in Euclidean spaces with realistic, infinite-range inter-particle and media-particle potentials featuring a power-law decay at infinity. Specifically, we prove that in an energy interval near the bottom of the spectrum, the spectral measure is pure point with probability one, and the decay rate of the averaged eigenfunction correlators in this energy interval admits a summable power-law bound, the exponent of which grows along with the growth of the decay exponents of the potentials. The localized eigen-functions admit a fractional-exponential bound on their decay rate. Earlier rigorous works on interactive Anderson models assumed the media-particle potential to be compactly supported.