  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.
