### Abstract

Original language | English |
---|---|

Pages (from-to) | 357-369 |

Number of pages | 13 |

Journal | Journal of Statistical Physics |

Volume | 59 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Apr 1990 |

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### Cite this

*Journal of Statistical Physics*,

*59*(1-2), 357-369. https://doi.org/10.1007/BF01015574

}

*Journal of Statistical Physics*, vol. 59, no. 1-2, pp. 357-369. https://doi.org/10.1007/BF01015574

**Inertial effects on the escape rate of a particle driven by colored noise : an instanton approach.** / Newman, T. J.; Bray, A. J.; McKane, A. J.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Inertial effects on the escape rate of a particle driven by colored noise

T2 - an instanton approach

AU - Newman, T. J.

AU - Bray, A. J.

AU - McKane, A. J.

PY - 1990/4

Y1 - 1990/4

N2 - A recent calculation, in the weak-noise limit, of the rate of escape of a particle over a one-dimensional potential barrier is extended by including an inertial term in the Langevin equation. Specifically, we consider a system described by the Langevin equation {Mathematical expression}, where ? is a Gaussian colored noise with mean zero and correlator =(D/t)exp(-|t-t'|/t). A pathintegral formulation is augmented by a steepest descent calculation valid in the weak-noise (D?0) limit. This yields an escape rate G~exp(-S/D), where the "action"S is the minimum, over paths characterizing escape over the barrier, of a generalized Onsager-Machlup functional, the extremal path being an "instanton" of the theory. The extremal action S is calculated analytically for small m and t for general potentials, and numerical results for S are displayed for various ranges of m and t for the typical case of the quartic potential V(x)=-x/2+x/4.

AB - A recent calculation, in the weak-noise limit, of the rate of escape of a particle over a one-dimensional potential barrier is extended by including an inertial term in the Langevin equation. Specifically, we consider a system described by the Langevin equation {Mathematical expression}, where ? is a Gaussian colored noise with mean zero and correlator =(D/t)exp(-|t-t'|/t). A pathintegral formulation is augmented by a steepest descent calculation valid in the weak-noise (D?0) limit. This yields an escape rate G~exp(-S/D), where the "action"S is the minimum, over paths characterizing escape over the barrier, of a generalized Onsager-Machlup functional, the extremal path being an "instanton" of the theory. The extremal action S is calculated analytically for small m and t for general potentials, and numerical results for S are displayed for various ranges of m and t for the typical case of the quartic potential V(x)=-x/2+x/4.

UR - http://www.scopus.com/inward/record.url?scp=5544262414&partnerID=8YFLogxK

U2 - 10.1007/BF01015574

DO - 10.1007/BF01015574

M3 - Article

VL - 59

SP - 357

EP - 369

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -