Rigorous results on Schroedinger operators with certain Gaussian random potentials in multi-dimensional continuous space

TL;DR

This paper proves that multi-dimensional Schroedinger operators with specific Gaussian random potentials almost surely have an absolutely continuous integrated density of states at low energies, indicating a form of spectral regularity.

Contribution

It provides rigorous mathematical results on the spectral properties of Schroedinger operators with Gaussian potentials in multiple dimensions, especially at low energies.

Findings

Almost sure absolute continuity of the integrated density of states

Absence of absolutely continuous spectrum at low energies

Spectral regularity in multi-dimensional Gaussian random potentials

Abstract

Schroedinger operators with certain Gaussian random potentials in multi-dimensional Euclidean space possess almost surely an absolutely continuous integrated density of states and no absolutely continuous spectrum at sufficiently low energies.