The density of states depends on the domain

TL;DR

This paper shows that the density of states for a Schrödinger operator with bounded potential varies depending on the domain chosen when taking the thermodynamic limit, highlighting domain dependence in spectral analysis.

Contribution

It reveals that the density of states is not an intrinsic property but depends on the domain, challenging assumptions in spectral theory of Schrödinger operators.

Findings

Density of states depends on the domain in the thermodynamic limit

Domain choice influences spectral properties of Schrödinger operators

Highlights importance of domain considerations in spectral analysis

Abstract

In this short note we demonstrate that the definition of the density of states of a Schr\"{o}dinger operator with bounded potential in general depends on the choice of the domain undergoing the thermodynamic limit.