Dixmier trace and the IDOS of perturbed magnetic operators
[Trace de Dixmier et IDOS des opérateurs magnétiques perturbés]
Belmonte, Fabián1 ; De Nittis, Giuseppe2
1Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta (Chile)
2Facultad de Matemáticas, & Instituto de Física, Pontificia Universidad, Católica de Chile, Santiago (Chile)
Annales de l'Institut Fourier, Online first, 54 p.

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 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.

L’objectif principal de ce travail est de fournir une description de la trace par unité de volume en termes de la trace de Dixmier (régularisée par la résolvante de l’oscillateur harmonique) pour une large classe d’opérateurs magnétiques bidimensionnels perturbés par des potentiels (homogènes). L’un des avantages de ce résultat est la possibilité de réinterpréter la densité d’états (DOS) de ces systèmes magnétiques perturbés au moyen de la trace de Dixmier, et de tirer parti du fait que cette quantité peut être calculée de manière pratique sur la base des fonctions de Laguerre qui diagonalisent l’oscillateur harmonique.

Reçu le :
Accepté le :
Première publication :
DOI : 10.5802/aif.3771
Classification : 81R15, 81V70, 58B34, 81R60
Keywords: Perturbed Landau Hamiltonian, IDOS and DOS, Dixmier trace
Mots-clés : Hamiltonien de Landau perturbé, IDOS et DOS, trace de Dixmier

Belmonte, Fabián  1   ; De Nittis, Giuseppe  2

1 Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta (Chile)
2 Facultad de Matemáticas, & Instituto de Física, Pontificia Universidad, Católica de Chile, Santiago (Chile) 
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Belmonte, Fabián; De Nittis, Giuseppe. Dixmier trace and the IDOS of perturbed magnetic operators. Annales de l'Institut Fourier, Online first, 54 p.

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