Critical exponents in metastable decay via quantum activation

Abstract

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 $η$ to the bifurcation point as $|\ln W|\propto η^ξ$. The exponent $ξ$ is found for a resonantly driven oscillator and an oscillator modulated at nearly twice its eigenfrequency.