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Dixmier trace and the DOS of magnetic operators · arXivDesk

2111.03410Nov 5, 202126 pages. Keywords: Landau Hamiltonian, IDOS and DOS, Dixmier trace, trace per unit volume

Dixmier trace and the DOS of magnetic operators

Fabian Belmonte, Giuseppe De Nittis

Abstract

The main goal of this work is to provide two new formulas for the computation of the trace per unit volume, and consequently the integrated density of states (IDOS), for magnetic operators. These formulas also permit the use of the Dixmier trace in the spectral analysis of magnetic operators. The second of these formulas, named energy shell formula, permits to approximate the IDOS by a finite sums of averaged expectation values of the spectral projections.

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The paper addresses: Dixmier trace and the DOS of magnetic operators.
The main goal of this work is to provide two new formulas for the computation of the trace per unit volume, and consequently the integrated density of states (IDOS), for magnetic operators.

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Author comment: 26 pages. Keywords: Landau Hamiltonian, IDOS and DOS, Dixmier trace, trace per unit volume

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