Multi-particle localization at low energy for the multi-dimensional continuous Anderson model
Year: 2017
Type: preprint
Abstract: We study the multi-particle 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 multi-particle lower edges of the spectrum 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 multi-particle Anderson model at low energy. The proof based on the multi-particle multi-scale analysis bounds, needs the values of the external random potential to be independent and identically distributed (i.i.d.) whose common probability distribution is at least Log-Hölder continuous.
Source: arXiv (Cornell University)
Author: Ekanga, Trésor
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2588048197