Localization at low energies for attractive Poisson random Schr\"odinger operators

TL;DR

This paper proves that attractive Poisson random Schr"odinger operators exhibit exponential and dynamical localization at low energies, ensuring finite multiplicity of eigenvalues in that spectral region across any dimension.

Contribution

It establishes low-energy localization and finite eigenvalue multiplicity for attractive Poisson random Schr"odinger operators in all dimensions, extending previous results.

Findings

Exponential localization at low energies

Dynamical localization at low energies

Finite multiplicity of eigenvalues

Abstract

We prove exponential and dynamical localization at low energies for the Schr\"odinger operator with an attractive Poisson random potential in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity.