Overdamped quantum phase diffusion and charging effects in Josephson junctions

By exploiting the recently derived quantum Smoluchowski equation, the classical Ivanchenko-Zil'berman theory for overdamped diffusive phase motion of low-capacitance Josephson junctions is extended to the low-temperature quantum domain where charging effects appear. This formulation allows to derive explicit results for the current-voltage characteristics over a broad range of parameters that reduce to known findings in certain limits. In particular, the transparent analytical approach comprises Coulomb-blockade physics, coherent Cooper-pair transfer, and the precursors of macroscopic quantum tunneling and needs to be supplemented by more sophisticated methods only at very low temperatures.