  Quantum decay rates for barrier potentials driven by external stochastic and
periodic forces in the strong damping regime are studied. Based on the recently
derived quantum Smoluchowski equation [Phys. Rev. Lett. {\bf 87}, 086802
(2001)] explicit analytical and numerical results are presented for the case of
the resonant activation phenomenon in a bistable potential and the escape from
a metastablwell with oscillating barrier, respectively. The significant impact
of quantum fluctuations is revealed.

Statistical Mechanics