  Motivated by experiments with current biased superconducting atomic point
contacts the general problem of nonadiabatic transitions between adiabatic
surfaces in presence of strong dissipation is studied. For a single channel
device the supercurrent is determined by the diffusive motion of the
superconducting phase difference on two Andreev levels. These surfaces are
uncoupled only in the adiabatic limit of low to moderate transmissions, while
for high transmissions curve crossings are important. Starting from a general
master equation of the full density matrix an approximate time evolution
equation for the populations on the adiabatic surfaces in the overdamped limit
is derived from which the relevant observables can be obtained. Specific
results for the case of atomic point contacts are in agreement with
experimental observations that cannot be explained by conventional theory.
