# Nonadiabatic escape and stochastic resonance

@article{Moon2019NonadiabaticEA, title={Nonadiabatic escape and stochastic resonance}, author={Woosok Moon and Neil J. Balmforth and John S. Wettlaufer}, journal={arXiv: Statistical Mechanics}, year={2019} }

We analyze the fluctuation-driven escape of particles from a metastable state under the influence of a weak periodic force. We develop an asymptotic method to solve the appropriate Fokker-Planck equation with mixed natural and absorbing boundary conditions. The approach uses two boundary layers flanking an interior region; most of the probability is concentrated within the boundary layer near the metastable point of the potential and particles transit the interior region before exiting the… Expand

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#### References

SHOWING 1-10 OF 55 REFERENCES

TIME OSCILLATIONS OF ESCAPE RATES IN PERIODICALLY DRIVEN SYSTEMS

- Physics
- 1999

We provide an explicit solution of the problem of activation escape from a metastable state of a periodically driven Brownian particle, including both the exponent and the prefactor. We find the… Expand

Periodically driven stochastic systems

- Physics
- 1993

Abstract Activation processes in classical metastable systems in the presence of periodic driving have recently become subject of growing research activity, stimulated by exciting new phenomena such… Expand

Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach

- Mathematics
- 2005

Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is… Expand

Theory of stochastic resonance.

- Physics, Medicine
- Physical review. A, General physics
- 1989

A detailed theoretical and numerical study of stochastic resonance, based on a rate equation approach, results in an equation for the output signal-to-noise ratio as a function of the rate at which noise induces hopping between the two states. Expand

Universality of first-passage- and residence-time distributions in non-adiabatic stochastic resonance

- Physics, Mathematics
- 2004

We present mathematically rigorous expressions for the first-passage-time and residence-time distributions of a periodically forced Brownian particle in a bistable potential. For a broad range of… Expand

Thermal activation in bistable systems under external periodic forces

- Physics
- 1989

Considered is the motion of a Brownian particle in a bistable potential exposed to an external periodic field. Our analysis is based on a systematic Fokker-Planck description of the non-stationary… Expand

A practical difference scheme for Fokker-Planck equations☆

- Mathematics
- 1970

A practical finite difference scheme for initial value problems of Fokker-Planck equations has been studied. In addition to satisfying the conditions of convergence and unconditional stability, this… Expand

Surmounting oscillating barriers

- Physics, Medicine
- Physical review letters
- 2000

Novel time-dependent path-integral methods are used to derive asymptotically exact weak-noise expressions for both the instantaneous and the time-averaged escape rate of thermally activated escape over a potential barrier. Expand

Reaction-rate theory: fifty years after Kramers

- Physics
- 1990

The calculation of rate coefficients is a discipline of nonlinear science of importance to much of physics, chemistry, engineering, and biology. Fifty years after Kramers' seminal paper on thermally… Expand

A Primer on Noise-Induced Transitions in Applied Dynamical Systems

- Physics, Mathematics
- SIAM Rev.
- 2018

An overview of the theory underlying the dynamics of rare events for stochastic models along with some example applications is provided. Expand