Quantum circuit theory and measurements on Y-Ba-Cu-O grain-boundary weak-link bridges

The quantum system associated with a resistor-shunted weak-link junction circuit may be described in terms of a single Lagrangian. In this representation the degrees of freedom internal to the dissipative energy of the resistor can be systematically separated from the Hamiltonian formulation of the circuit. This allows us to solve the quantum states of the junction while the effects of the resistor on the circuit are included as a Lagrangian multiplier. In this manner the effects of the measuring apparatus or resistor on the quantum state of the junction may be calculable. The calculations are in very good agreement with experiments