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arXiv · 2312.08294

Dixmier trace and the DOS of perturbed magnetic operators

Fabian Belmonte·Giuseppe De Nittis
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Abstract

The main goal of this work is to provide a description of the {trace per unit volume} in terms of the {Dixmier trace} (regularized by the resolvent of the harmonic oscillator) for a large class of two-dimensional \emph{magnetic operators} perturbed by (homogeneous) {potentials}. One of the payoffs of this result is the possibility of reinterpreting the {density of states} (DOS) of these perturbed magnetic systems via the {Dixmier trace}, and taking advantage of the fact that this quantity can be conveniently calculated on the basis of the Laguerrre functions that diagonalize the harmonic oscillator.

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Fabian Belmonte, Giuseppe De Nittis. 2023-12-13. Dixmier trace and the DOS of perturbed magnetic operators. https://arxiv.org/abs/2312.08294

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