F.Bentosela, P. Exner, V.A. Zagrebnov
Anomalous electron trapping by magnetic flux tubes and
electric current vortices
(19K, LaTeX)
ABSTRACT. We consider an electron with an anomalous magnetic
moment, g>2, confined to a plane and interacting with a
nonhomogeneous magnetic field B, and investigate the corresponding
Pauli Hamiltonian. We prove a lower bound on the number of bound
states for the case when B is of a compact support and the related
flux is N+\epsilon, \epsilon\in(0,1]. In particular, there are at
least N+1 bound states if B does not change sign. We also consider
the situation where the magnetic field is due to a localized
rotationally symmetric electric current vortex in the plane. In
this case the flux is zero; there is a pair of bound states for a
weak coupling, and higher orbital-momentum ``spin-down" states
appearing as the current strength increases. [This text will appear
in Proceedings of QMath7, Prague 1997 -- the final version replacing
mp_arc 98-695].