Aharonov-Bohm effect on the Poincaré disk

Abstract

We consider formal quantum hamiltonian of a charged particle on the Poincaré disk in the presence of an Aharonov-Bohm magnetic vortex and a uniform magnetic field. It is shown that this hamiltonian admits a four-parameter family of self-adjoint extensions. Its resolvent and the density of states are calculated for natural values of the extension parameters.

21 pages, 1 figure, references added

References in corpus (12)

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Cited by in corpus (4)

• Microstate Counting of $Ad{S}_4$ Hyperbolic Black Hole Entropy via the Topologically Twisted Index
• Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect
• On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk
• Quantum motion in superposition of Aharonov-Bohm with some additional electromagnetic fields