Schrödinger operators with multiple Aharonov-Bohm fluxes

Abstract

We study the Schrödinger operator describing a two-dimensional quantum particle moving in presence of $N⩾1$ Aharonov-Bohm magnetic fluxes. We classify all the self-adjont realizations of such an operator, providing an explicit characterization of their domains and actions. Moreover, we examine their spectral and scattering properties, proving in particular the existence and completeness of wave operators in relation with the free dynamics.

arXiv comment28 pages, pdfLaTeX, minor changes

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Cited by in corpus (3)

• Quadratic forms for Aharonov-Bohm Hamiltonians
• Deficiency indices for singular magnetic Schrödinger operators
• Aharonov-Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition