Indistinguishability of quantum states and rotation counting

TL;DR

This paper introduces a quantum system where the winding number of a particle on a ring becomes an observable, affecting the energy spectrum and reducing the magnetic flux period in the Aharonov-Bohm effect.

Contribution

It presents a novel quantum system that makes the winding number an observable and explores its impact on physical properties and flux periodicity.

Findings

Winding number can be monitored as a physical observable.

Orbital period extends to multiple rotations, altering energy spectrum.

Magnetic flux period reduces from  to /n.

Abstract

We propose a quantum system in which the winding number of rotations of a particle around a ring can be monitored and emerges as a physical observable. We explicitly analyze the situation when, as a result of the monitoring of the winding number, the period of the orbital motion of the particle is extended to $n>1$ full rotations, which leads to changes in the energy spectrum and in all observable properties. In particular, we show that in this case, the usual magnetic flux period $\Phi_0=h/q$ of the Aharonov-Bohm effect is reduced to $\Phi_0/n$.