Effect of quantum noise and tunneling on the fluctuational voltage-current characteristics and the lifetime of the zero-voltage state in Josephson junctions

The minima of the potential energy for the dynamical variable {φ} of a Josephson junction are separated by barriers of height {}Ic/e, where Ic is the critical current. At low temperatures, T{}{}Ic/e, the time-averaged voltage across the junction has its origin in thermally activated processes, which are more important than quantum tunneling if T>{}{Ω}/2{π} ({Ω} is the Josephson plasma frequency). We consider this problem for high-quality junctions (RC{Ω}{}1, R and C are the resistance and the capacitance of the junction), accounting for the effect of a Johnson-Nyquist noise and quantum tunneling at the barrier top. With a simplifying assumption, we derive a pair of integral equations containing an energy variable for the steady-state distribution of {φ} and {φ} ̇ \.{}{}, and solve it by a modification of the Wiener-Hopf method. The result is a formula for the current dependence of the fluctuational voltage, valid for currents I4Ic/{π}RC{Ω}. We discuss the ohmic resistance of the junction, the case of a relatively high damping (1{}RC{Ω}{}{}Ic/T), the classical limit {}{Ω}/T{→}0, and perturbative quantum corrections in ({}{Ω}/T)²{}1. At currents I{}Ic and I{}Ic/RC{Ω},eT/{} we obtain an expression for the lifetime {τ} of the zero-voltage state. Numerical results for {τ} are also presented.