Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic Schrodinger operators

TL;DR

This paper establishes a comprehensive asymptotic expansion for the integrated density of states of multidimensional Schrödinger operators with various classes of almost-periodic potentials, advancing spectral theory understanding.

Contribution

It provides the first complete asymptotic expansion for the integrated density of states in multidimensional almost-periodic Schrödinger operators, covering periodic, quasi-periodic, and broad almost-periodic potentials.

Findings

Asymptotic expansion is valid for smooth periodic potentials.

Extension to generic quasi-periodic potentials.

Applicable to a wide class of almost-periodic functions.

Abstract

We prove the complete asymptotic expansion of the integrated density of states of a Schrodinger operator H = -\Delta + b acting in R^d when the potential b is either smooth periodic, or generic quasi-periodic (finite linear combination of exponentials), or belongs to a wide class of almost-periodic functions.