Anomalous electron trapping by localized magnetic fields

Details Anomalous electron trapping by localized magnetic fields Anomalous electron trapping by localized magnetic fields

1999-03-13

arxiv.org/abs/math-ph/9903030v1

J. Phys. A32 (1999), 3029-3039

Physics

Mathematical Physics

A LaTeX file, 12 pages; to appear in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/32/16/011

We consider an electron with an anomalous magnetic moment g>2 confined to a plane and interacting with a nonzero magnetic field B perpendicular to the plane. We show that if B has compact support and the magnetic flux in the natural units is F\ge 0, the corresponding Pauli Hamiltonian has at least 1+[F] bound states, without making any assumptions about the field profile. Furthermore, in the zero-flux case there is a pair of bound states with opposite spin orientations. Using a Birman-Schwinger technique, we extend the last claim to a weak rotationally symmetric field with B(r) = O(r^{-2-\delta}) correcting thus a recent result. Finally, we show that under mild regularity assumptions the existence can be proved for non-symmetric fields with tails as well.

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