We have observed a dissipative phase diffusion branch in arrays of hysteretic high-T-c intrinsic Josephson junctions. By comparing the data with a thermal activation model we extract the impedance seen by the junction in which phase diffusion is occurring. At the plasma frequency this junction is isolated from its environment and it sees its own large (similar to kOmega) impedance. Our results suggest that stacks of Josephson junctions may be used for isolation purposes in the development of a solid state quantum computer.
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