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 Phi and Phi + 2 pi are indistinguishable. We show that interactions with another particle on a neighboring ring can modify the configuration space and make the points Phi and Phi + 2 pi distinguishable. As a consequence, the orbital motion acquires a periodicity of 2 pi n with n > 1 which leads to changes in the energy spectrum and in all observable properties. In particular, the fundamental magnetic flux period Phi(0) = h/q of the Aharonov-Bohm effect is reduced to 443, Phi(0)/n.