### Abstract

The path-integral formalism developed in the preceding paper [McKane, Luckock, and Bray, Phys. Rev. A 41, 644 (1990)] is used to calculate, in the weak-noise limit, the rate of escape of a particle over a one-dimensional potential barrier, for exponentially correlated noise (t)(t) =(D/)exp{-t-t/}. For small D, a steepest-descent evaluation of the appropriate path integral yields exp(-S/D), where S is the action associated with the dominant (instanton) path. Analytical results for S are obtained for small and large , and (essentially exact) numerical results for intermediate. The stationary joint probability density for the position and velocity of the particle is also calculated for small D: it has the form Pst (x,xI)exp[-S(x,xI)/D]. Results are presented for the marginal probability density Pst(x) for the position of the particle.

Original language | English |
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Pages (from-to) | 657-667 |

Number of pages | 11 |

Journal | Physical Review A |

Volume | 41 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1990 |

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## Cite this

Bray, A. J., McKane, A. J., & Newman, T. J. (1990). Path integrals and non-Markov processes. II. Escape rates and stationary distributions in the weak-noise limit.

*Physical Review A*,*41*(2), 657-667. https://doi.org/10.1103/PhysRevA.41.657