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

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

Cet article étudie le comportement asymptotique des valeurs propres négatives <-λ, quand λ→+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(λ)=(1/2π)∫ V(x)>λ b(x)dx(1+o(1)), quand V(x) diminue plus rapidement que b(x) 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},
     pages = {479--515},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {48},
     number = {2},
     year = {1998},
     doi = {10.5802/aif.1626},
     zbl = {0909.35100},
     mrnumber = {99e:35168},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1626/}
}
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Iwatsuka, Akira; Tamura, Hideo. Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields. Annales de l'Institut Fourier, Tome 48 (1998) no. 2, pp. 479-515. doi: 10.5802/aif.1626

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