Pauli Hamiltonians with an Aharonov-Bohm Flux

Abstract

We study a two-dimensional Pauli operator describing a charged quantum particle with spin $1/2$ moving on a plane in presence of an orthogonal Aharonov-Bohm magnetic flux. We classify all the admissible self-adjont realizations and give a complete picture of their spectral and scattering properties. Symmetries of the resulting Hamiltonians are also discussed, as well as their connection with the Dirac operator perturbed by an Aharonov-Bohm singularity.

33 pages, pdfLaTeX, slightly enlarged and updated with respect to the previous version, to appear in J. Spectr. Theory. Prop. 2.26 corrected and Remark 2.27 added. Additional minor modifications

References in corpus (5)

• Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
• On the Dirac and Pauli operators with several Aharonov-Bohm solenoids
• On domain properties of Bessel-type operators
• Quadratic forms for Aharonov-Bohm Hamiltonians
• Semiclassical spectrum of the Dirichlet-Pauli operator on an annulus

Cited by in corpus (3)

• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Aharonov-Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition
• On two-dimensional Dirac operators with critical delta-shell interactions