  We report the solution of the persistent current in two coupled rings in the
presence of external magnetic fluxes. We showed that the magnetic fluxes modify
the global phase of the electronic wave function for multiple connected
geometry formed by the coupled rings. We obtained an exact solution for the
persistent current and investigated the exact solution numerically. For two
large coupled rings with equal fluxes, we found that the persistent current in
the two coupled rings is in fact equal to that in a single ring. This theory
explains the experimental results observed in a line of sixteen coupled rings.
(Phys. Rev. Lett. 86, 3124 (2001).)
