  We discuss the dynamics of a Bose-Einstein condensate in a double-well trap
subject to phase noise and particle loss. The phase coherence of a
weakly-interacting condensate as well as the response to an external driving
show a pronounced stochastic resonance effect: Both quantities become maximal
for a finite value of the dissipation rate matching the intrinsic time scales
of the system. Even stronger effects are observed when dissipation acts in
concurrence with strong inter-particle interactions, restoring the purity of
the condensate almost completely and increasing the phase coherence
significantly.
