Aspects of classical and quantum motion on a flux cone

Motion of a nonrelativistic 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. The probability fluid (“quantum flow”) associated with a particular stationary state is studied close to the singularity, demonstrating nontrivial 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 analyzed. It is shown that the winding number of classical orbits plays a role in the description of the quantum flow. The connectivity of the configuration space is also discussed.