Critical exponents in metastable decay via quantum activation

We consider decay of metastable states of forced vibrations of a quantum oscillator close to bifurcation points, where dissipation becomes effectively strong. We show that decay occurs via quantum activation over an effective barrier. The decay probability $W$ scales with the distance $\eta$ to the bifurcation point as $|\ln W|\propto \eta^{\xi}$. The exponent $\xi$ is found for a resonantly driven oscillator and an oscillator modulated at nearly twice its eigenfrequency.