Magnetization of two coupled rings
  We investigate the persistent currents and magnetization of a mesoscopic system consisting of two clean metallic rings sharing a single contact point in a magnetic field. Many novel features with respect to the single-ring geometry are underlined, including the explicit dependence of wavefunctions on the Aharonov-Bohm fluxes, the complex pattern of twofold and threefold degeneracies, the key role of length and flux commensurability, and in the case of commensurate ring lengths the occurrence of idle levels which do not carry any current. Spin-orbit interactions, induced by the electric fields of charged wires threading the rings, give rise to a peculiar version of the Aharonov-Casher effect where, unlike for a single ring, spin is not conserved. Remarkably enough, this can only be realized when the Aharonov-Bohm fluxes in both rings are neither integer nor half-integer multiples of the flux quantum. 
Y. Avishai and J.M. Luck