Multiparticle Localization at Low Energy for Multidimensional Continuous Anderson Models

Abstract EN

We study the multiparticle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multiparticle lower spectral edges are almost surely constant in absence of ergodicity.

We stress that this result is not quite obvious and has to be handled carefully.

In addition, we prove the spectral exponential and the strong dynamical localization of the continuous multiparticle Anderson model at low energy.

The proof based on the multiparticle multiscale analysis bounds needs the values of the external random potential to be independent and identically distributed, whose common probability distribution is at least Log-Hölder continuous.