On the Vortex-Point Charge Composite: Classical Orbits and Quantum Bound States

TL;DR

This paper explores the classical and quantum bound states of a point charge interacting with a vortex in 2+1 dimensions, revealing conditions for stable or metastable states and addressing Hamiltonian self-adjointness issues.

Contribution

It introduces a semi-classical analysis of the vortex-charge system, identifying parameter ranges for bounded orbits and bound states, and discusses the mathematical conditions for quantum stability.

Findings

Classical bounded orbits exist for specific parameters.

Metastable states are identified via effective potential analysis.

Self-adjoint extensions of the Hamiltonian lead to quantum bound states.

Abstract

The possibility of composite systems arising out of a point charge interacting with a Nielsen-Olesen vortex in 2+1-dimensions is investigated. It is shown that classical bounded orbits are possible for certain ranges of parameters. Long lived metastable states are shown to exist, in a semi-classical approach, from the study of the effective potential. Loss of self-adjointness of the Hamiltonian and its subsequent self-adjoint extension in some cases leads to bound states.