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arXiv · 1910.12380

A Dixmier trace formula for the density of states

Nurulla Azamov·Edward McDonald·Fedor Sukochev·Dmitriy Zanin
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Abstract

A version of Connes trace formula allows to associate a measure on the essential spectrum of a Schr\"odinger 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.

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Nurulla Azamov, Edward McDonald, Fedor Sukochev, Dmitriy Zanin. 2019-10-27. A Dixmier trace formula for the density of states. https://doi.org/10.1007/s00220-020-03756-7

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