Enhancement of the decay rate of a metastable state by an external driving force

Abstract

The effect of a sinusoidal force on the rate of thermally activated escape of a damped particle from a metastable potential well is examined. The analysis is carried out for a damping coefficient with arbitrary frequency dependence and for a potential well of arbitrary form. It is assumed that for large-amplitude oscillations in the well the average changes of the energy per oscillation period due to damping and due to the driving force are much smaller than the energy of the particle. Under these conditions, the escape is resonantly activated when the frequency of the applied force approximately equals multiples of the natural frequency at which the particle oscillates at the bottom of the well. Due to the anharmonicity of the potential, the resonances are of highly asymmetric shape. Specific results are given for a model appropriate to a current-biased Josephson tunnel junction in its zero-voltage state. The theory describes the observed microwave-enhanced escape from the zero-voltage state for microwave frequencies near the plasma frequency. The long low-frequency tail of the resonance, the sharp high-frequency rolloff and the behavior near the peak are predicted correctly. Detailed predictions are also made for the size and for the shape of the second resonance, and a sum rule for the activation factor is obtained.