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

Akira Iwatsuka; Hideo Tamura — 1998

Annales de l'institut Fourier

This article studies the asymptotic behavior of the number $N (λ)$ of the negative eigenvalues $< - λ$ as $λ \to + 0$ 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 $N (λ) = (1 / 2 π) \int_{V (x) > λ} b (x) d x (1 + o (1))$ , when $V (x)$ decays faster than $b (x)$ under some additional conditions.

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