Indistinguishability of quantum states and rotation counting

We consider a system that is effectively a quantum particle on a one-dimensional ring for which the points φ and φ+2π are indistinguishable. We show that interactions with another particle on a neighboring ring can modify the configuration space and make the points φ and φ+2π distinguishable. As a consequence, the orbital motion acquires a periodicity of 2πn with n>1 which leads to changes in the energy spectrum and in all observable properties. In particular, the fundamental magnetic flux period Φ0=h/q of the Aharonov-Bohm effect is reduced to Φ0/n.