  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.
