Aspects of classical and quantum motion on a flux cone

TL;DR

This paper investigates the classical and quantum dynamics of a particle on a flux cone, revealing non-trivial Aharonov-Bohm effects and the influence of conical singularities on quantum flow and potential.

Contribution

It provides a detailed analysis of quantum flow near conical singularities and explores the impact of topology and flux on particle motion, advancing understanding of quantum behavior in singular geometries.

Findings

Quantum flow departs from classical flow near the singularity.

Quantum potential due to the conical singularity influences quantum flow.

Winding number affects the quantum flow description.

Abstract

Motion of a non-relativistic particle on a cone with a magnetic flux running through the cone axis (a ``flux cone'') is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. Probability fluid (``quantum flow'') associated with a particular stationary state is studied close to the singularity, demonstrating non trivial Aharonov-Bohm effects. For example, it is shown that near the singularity quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential due to the conical singularity is determined and the way it affects quantum flow is analysed. It is shown that the winding number of classical orbits plays a role in the description of the quantum flow. Connectivity of the configuration space is also discussed.