Anomalous electron trapping by magnetic flux tubes and electric current vortices
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.
- Publication:
-
Mathematical Results in Quantum Mechanics
- Pub Date:
- 1999
- DOI:
- 10.48550/arXiv.math-ph/9810016
- arXiv:
- arXiv:math-ph/9810016
- Bibcode:
- 1999mrqm.conf..191B
- Keywords:
-
- Mathematical Physics;
- Condensed Matter;
- Mathematics - Mathematical Physics;
- Quantum Physics
- E-Print:
- 6 pages, LaTeX, to appear in Proceedings of QMath7, Prague 1997, published in the Birkhauser series "Operator Theory: Advances and Applications