A Dixmier Trace Formula for the Density of States

A Dixmier Trace Formula for the Density of States

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 mea...

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Veröffentlicht in:Communications in mathematical physics 2020-08, Vol.377 (3), p.2597-2628
Hauptverfasser: Azamov, N., McDonald, E., Sukochev, F., Zanin, D.
Format: Artikel
Sprache:eng
Schlagworte:
Classical and Quantum Gravitation
Complex Systems
Density of states
Mathematical and Computational Physics
Mathematical Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Solid state physics
Theoretical
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Zusammenfassung: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03756-7