Zero modes for the magnetic Pauli operator in even-dimensional Euclidean space

Details Zero modes for the magnetic Pauli operator in even-dimensional Euclidean space Zero modes for the magnetic Pauli operator in even-dimensional Euclidean space

2007-10-22

arxiv.org/abs/0710.3992v1

Mathematics

Spectral Theory

13 pages

Scientific paper

10.1007/s11005-008-0265-4

We study the ground state of the Pauli Hamiltonian with a magnetic field in R^(2d). We consider the case where a scalar potential W is present and the magnetic field B is given by $B=2i\partial\bar\partial W$. The main result is that there are no zero modes if the magnetic field decays faster than quadratically at infinity. If the magnetic field decays quadratically then zero modes may appear, and we give a lower bound for the number of them. The results in this paper partly correct a mistake in a paper from 1993.

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