We study multiple eigenvalues of a magnetic Aharonov–Bohm operator with Dirichlet boundary conditions in a planar domain. In particular, we study the structure of the set of the couples position of the pole-circulation which keep fixed the multiplicity of a double eigenvalue of the operator with the pole at the origin and half-integer circulation. We provide sufficient conditions for which this set is made of an isolated point. The result confirms and validates a lot of numerical simulations available in preexisting literature.

On multiple eigenvalues for Aharonov–Bohm operators in planar domains

Abatangelo L.;
2018-01-01

Abstract

We study multiple eigenvalues of a magnetic Aharonov–Bohm operator with Dirichlet boundary conditions in a planar domain. In particular, we study the structure of the set of the couples position of the pole-circulation which keep fixed the multiplicity of a double eigenvalue of the operator with the pole at the origin and half-integer circulation. We provide sufficient conditions for which this set is made of an isolated point. The result confirms and validates a lot of numerical simulations available in preexisting literature.
2018
Aharonov–Bohm potential
Magnetic Schrödinger operators
Multiple eigenvalues
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1180552
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