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Surmounting Oscillating Barriers: Path-integral approach for Weak Noise

Jörg Lehmann·Peter Reimann·Peter Hänggi
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Abstract

We consider the thermally activated escape of an overdamped Brownian particle over a potential barrier in the presence of periodic driving. A time-dependent path-integral formalism is developed which allows us to derive asymptotically exact weak-noise expressions for both the instantaneous and the time-averaged escape rate. Our results comprise a conceptionally new, systematic treatment of the rate prefactor multiplying the exponentially leading Arrhenius factor. Moreover, an estimate for the deviations at finite noise-strengths is provided and a supersymmetry-type property of the time averaged escape rate is verified. For piecewise parabolic potentials, the rate-expression can be evaluated in closed analytical form, while in more general cases, as exemplified by a cubic potential, an action-integral remains to be minimized numerically. Our comparison with very accurate numerical results demonstrates an excellent agreement with the theoretical predictions over a wide range of driving strengths and driving frequencies.

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Jörg Lehmann, Peter Reimann, Peter Hänggi. 2000-07-12. Surmounting Oscillating Barriers: Path-integral approach for Weak Noise. https://doi.org/10.1103/physreve.62.6282

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