Quantum phase fluctuation in high T-c superconductors

If phase coherence determines the superconducting transition temperature T- c in the cuprate oxides, it is of great interest to understand the role tha t dynamics of the:phase fluctuation plays in bringing about depletion of th e superconducting condensate. We will show that a phase correlation functio n can be calculated that allows us to describe depletion of superconducting condensate as a result of the quantum fluctuation. The vanishing of Andree v conductivity at a critical votage below the superconducting gap will be s hown as resulting from voltage induced phase excitation and dephasing.