Abstract
We study the dynamics of the phase of a resistively shunted single Josephson junction in the extreme quantum limit. The problem corresponds to that of a quantum mechanical Brownian particle in a tilted washboard potential. An exact series representation in powers of the tunnel matrix element Δ for moments 〈φ n 〉 of the phase φ is given. The dynamics at zero and at finite temperatures is solved exactly to all orders of Δ for a particular value of the dimensionless friction α ≡ h (4e 2R) = 1 2 and also for very weak damping α ⪡ 1.
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