Equilibrium currents in quantum double ring system: A non-trivial role of system-reservoir coupling

Amperes law states that the magnetic moment of a ring is given by current times the area enclosed. Also from equilibrium statistical mechanics it is known that magnetic moment is the derivative of free energy with respect to magnetic field. In this work we analyze a quantum double ring system interacting with a reservoir. A simple S-Matrix model is used for system-reservoir coupling. We see complete agreement between the aforesaid two definitions when coupling between system and reservoir is weak, increasing the strength of coupling parameter however leads to disagreement between the two. Thereby signifying the important role played by the coupling parameter in mesoscopic systems.