Quantum and thermal fluctuations in the dynamics of a RCSJ junction

We theoretically investigate the phase and voltage correlation dynamics under a current noise including thermal and quantum fluctuations in a resistively and capacitively shunted Josephson (RCSJ) junction. Within the linear regime, an external current is found to shift and intensify the deterministic contributions in phase and voltage. In addition to the deterministic contribution, we observe the relaxation of autocorrelation functions of phase and voltage to finite values due to the current noise. We also find an earlier decay of coherence at a higher temperature in which thermal fluctuations dominate over quantum ones.