Quantum dissipative behaviour of a superconducting weak link constriction ring

We analyze the flux mode regime in a superconducting ring closed with a Josephson junction by means of a Feynman path-integral treatment. We derive the propagator for the quantum dissipative system, when a damping term in the Anderson-Josephson lagrangian is included. The wavefunctions and the energy levels are obtained from this propagator. Agreement with the exact results for the undamped case is discussed. Once found, the classical limit appears to be a formal way to obtain a relation between the conjugate variables for the weak link. The requirements of the equivalence between Feynman's and Schrodinger's approach allow to speculate on the Feynman path differential measure in flux space for the system under consideration.