Infiniteness of zero modes for the Pauli operator with singular magnetic field

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We establish that the Pauli operator describing a spin-1/2 two-dimensional quantum system with a singular magnetic field has, under certain conditions, an infinite-dimensional space of zero modes, possibly, both spin-up and spin-down, moreover there is a spectral gap separating the zero eigenvalue from the rest of the spectrum. In particular, infiniteness takes place if the field has infinite flux, which settles this previously unknown case of Aharonov-Casher theorem.

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Mathematical Physics, 81Q10; 47N50; 47F05;35Q40;35P15

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http://salesiana.dossiersoluciones.com/handle/123456789/57966

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0501059
 http://arxiv.org/abs/math-ph/0501059

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arXiv