Quantum and thermal fluctuations in the dynamics of a resistively and capacitively shunted Josephson junction

We theoretically investigate the phase and voltage correlation dynamics, which includes both deterministic contribution stochastic fluctuations, under a current noise generated by resistor including thermal quantum fluctuations in resistively capacitively shunted Josephson junction. An external is found to shift intensify contributions voltage. In addition effects of current, we observe relaxation autocorrelation functions voltage, variances due noise, finite values long-time limit. particular, find that asymptotic correlations depend on resistance as consequence effects. also an earlier decay coherence at higher temperature dominate over ones. These theoretical predictions can be tested next future experiments.