Overdamped quantum phase diffusion and charging effects in Josephson junctions

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.