Aharonov-Bohm effect on the Poincar\'e disk

TL;DR

This paper investigates the quantum behavior of a charged particle on the Poincaré disk influenced by an Aharonov-Bohm vortex and a uniform magnetic field, analyzing self-adjoint extensions and spectral properties.

Contribution

It introduces a four-parameter family of self-adjoint extensions for the Hamiltonian and computes its resolvent and density of states.

Findings

Explicit resolvent formulas derived

Density of states calculated for natural extension parameters

Self-adjoint extension parameters characterized

Abstract

We consider formal quantum hamiltonian of a charged particle on the Poincar\'e 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.