Magnetic Perturbations of Anyonic and Aharonov-Bohm Schrödinger Operators

Abstract

We study the Hamiltonian describing two anyons moving in a plane in presence of an external magnetic field and identify a one-parameter family of self-adjoint realizations of the corresponding Schrödinger operator. We also discuss the associated model describing a quantum particle immersed in a magnetic field with a local Aharonov-Bohm singularity. For a special class of magnetic potentials, we provide a complete classification of all possible self-adjoint extensions.

arXiv comment28 pages, final version, to appear in J. Math. Phys., pdfLaTex

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Cited by in corpus (6)

• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Properties of 2D anyon gas
• A Lieb-Thirring inequality for extended anyons
• Quadratic forms for Aharonov-Bohm Hamiltonians
• Diffraction of the Aharonov-Bohm Hamiltonian
• Deficiency indices for singular magnetic Schrödinger operators