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Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field

Pavel Exner·Pavel Stovicek·Petr Vytras
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Abstract

The most general admissible boundary conditions are derived for an idealised Aharonov-Bohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; other two parameters of the model are the Aharonov-Bohm flux and the homogeneous magnetic field. The generalised boundary conditions may be regarded as a combination of the Aharonov-Bohm effect with a point interaction. Spectral properties of the derived Hamiltonians are studied in detail.

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Pavel Exner, Pavel Stovicek, Petr Vytras. 2001-11-08. Generalised boundary conditions for the Aharonov-Bohm effect combined with a homogeneous magnetic field. https://doi.org/10.1063/1.1463712

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