A Dixmier trace formula for the density of states

Abstract

A version of Connes trace formula allows to associate a measure on the essential spectrum of a Schrödinger operator with bounded potential. In solid state physics there is another celebrated measure associated with such operators --- the density of states. In this paper we demonstrate that these two measures coincide. We show how this equality can be used to give explicit formulae for the density of states in some circumstances.

References in corpus (4)

• Operator Lipschitz Functions
• Bounds on the density of states for Schr\" odinger operators
• Cwikel estimates revisited
• Trace theorem for quasi-Fuchsian groups

Cited by in corpus (7)

• The Geometry of (non-Abelian) Landau levels
• The Noncommutative Geometry of the Landau Hamiltonian: Metric Aspects
• An Application of Singular Traces to Crystals and Percolation
• Dixmier trace and the DOS of magnetic operators
• The noncommutative geometry of the Landau Hamiltonian: Differential aspects
• A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity
• Spectral flow inside essential spectrum V: on absorbing points of coupling resonances