Dixmier trace and the DOS of perturbed magnetic operators
Mathematical Physics
2023-12-14 v1 Mesoscale and Nanoscale Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2312.08294,
title = {Dixmier trace and the DOS of perturbed magnetic operators},
author = {Fabian Belmonte and Giuseppe De Nittis},
journal= {arXiv preprint arXiv:2312.08294},
year = {2023}
}
Comments
47 pages. Keywords: Perturbed Landau Hamiltonian, IDOS and DOS, Dixmier trace, trace per unit volume