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

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

2005-01-24

arxiv.org/abs/math-ph/0501059v1

Physics

Mathematical Physics

Scientific paper

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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