Effect of time-delayed friction on the escape from a metastable well

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Abstract
The rate for thermally activated escape from a cubic metastable well is investigated. The escape rate can become substantially smaller than its transition-state-theory limit either for strong damping, where the slow spatial diffusion across the barrier top diminishes the rate, or for very weak damping, where the rate is reduced because of the slow repopulation of the highly excited states in the well. It is shown that for a system with time-delayed friction the two regions can clearly be distinguished. For spatial-diffusion-limited decay, the rate shows a monotonic dependence on the delay time, while for energy-diffusion-limited decay the rate exhibits oscillatory behavior. Calculations are performed for a specific model which is suitable to describe the decay of the zero-voltage state of a Josephson junction shunted by a transmission line with variable effective length.