Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields
Annales de l'Institut Fourier, Volume 48 (1998) no. 2, p. 479-515

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

Cet article étudie le comportement asymptotique des valeurs propres négatives $<-\lambda$, quand $\lambda \to +0$, des opérateurs de Pauli avec un potentiel électrique $V\left(x\right)$ 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 $N\left(\lambda \right)=\left(1/2\pi \right){\int }_{V\left(x\right)>\lambda }b\left(x\right)dx\left(1+o\left(1\right)\right)$, quand $V\left(x\right)$ diminue plus rapidement que $b\left(x\right)$ sous des hypothèses supplémentaires.

@article{AIF_1998__48_2_479_0,
author = {Iwatsuka, Akira and Tamura, Hideo},
title = {Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {48},
number = {2},
year = {1998},
pages = {479-515},
doi = {10.5802/aif.1626},
zbl = {0909.35100},
mrnumber = {99e:35168},
language = {en},
url = {http://www.numdam.org/item/AIF_1998__48_2_479_0}
}

Iwatsuka, Akira; Tamura, Hideo. Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields. Annales de l'Institut Fourier, Volume 48 (1998) no. 2, pp. 479-515. doi : 10.5802/aif.1626. http://www.numdam.org/item/AIF_1998__48_2_479_0/

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