Localization for one-dimensional two-particle random Schr\"odinger operators with Poisson potential

TL;DR

This paper proves Anderson localization for a two-particle one-dimensional Schrödinger operator with Poisson potential, demonstrating spectral and dynamical localization under weak interactions.

Contribution

It establishes the first comprehensive proof of spectral and dynamical localization for two-particle systems with Poisson potential and weak interactions.

Findings

Complete spectral localization established

Strong dynamical localization proven

Results applicable to weakly interacting particle systems

Abstract

We prove the complete spectral and the strong dynamical Anderson localization in a two-particle random Schr\"odinger operators with the Poisson potential. The results apply with sufficiently weak interaction between the particle system.