Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields

Iwatsuka, Akira ; Tamura, Hideo

Annales de l'Institut Fourier, Tome 48 (1998), p. 479-515 / Harvested from Numdam

Résumé

Cet article étudie le comportement asymptotique des valeurs propres négatives $< -\lambda $, quand $\lambda \rightarrow +0$, des opérateurs de Pauli avec un potentiel électrique $V(x)$ qui tend vers $0$ à l’infini et avec un champ magnétique non constant, qui est supposé borné ou tendant vers $0$ à l’infini. Il est montré, en particulier, que $N(\lambda ) = (1/2\pi ) \int _{V(x)>\lambda }b(x)dx(1+o(1))$, quand $V(x)$ diminue plus rapidement que $b(x)$ sous des hypothèses supplémentaires.

Abstract

This article studies the asymptotic behavior of the number $N(\lambda )$ of the negative eigenvalues $< -\lambda $ as $\lambda \rightarrow +0$ of the two dimensional Pauli operators with electric potential $V(x)$ decaying at $\infty $ and with nonconstant magnetic field $b(x)$, which is assumed to be bounded or to decay at $\infty $. In particular, it is shown that $N(\lambda ) = (1/2\pi ) \int _{V(x)>\lambda }b(x)dx(1+o(1))$, when $V(x)$ decays faster than $b(x)$ under some additional conditions.

Détail

Publié le : 1998-01-01

MR 99e:35168 | Zbl 0909.35100 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.1626

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