### Abstract

The projection-operator method is used to find a Fokker-Planck equation with a time-dependent diffusion coefficient. It is shown that this equation is correct under a precise condition of small noise intensity and can be used successfully to study the problem of escape over the potential barrier of a bistable system. An exact expression for the first-passage time for , is found, where is the noise correlation time. It is then shown with a numerical method that the Fokker-Planck equation relying on the assumption of local linearization bridges the exact limit for , and the standard one for =0. Some intriguing aspects of the short- region are discussed.

Original language | English |
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Pages (from-to) | 3749-3757 |

Number of pages | 9 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 38 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*38*(7), 3749-3757. https://doi.org/10.1103/PhysRevA.38.3749

**Escape over a potential barrier in the presence of colored noise : Predictions of a local-linearization theory.** / Tsironis, George P.; Grigolini, Paolo.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 38, no. 7, pp. 3749-3757. https://doi.org/10.1103/PhysRevA.38.3749

}

TY - JOUR

T1 - Escape over a potential barrier in the presence of colored noise

T2 - Predictions of a local-linearization theory

AU - Tsironis, George P.

AU - Grigolini, Paolo

PY - 1988

Y1 - 1988

N2 - The projection-operator method is used to find a Fokker-Planck equation with a time-dependent diffusion coefficient. It is shown that this equation is correct under a precise condition of small noise intensity and can be used successfully to study the problem of escape over the potential barrier of a bistable system. An exact expression for the first-passage time for , is found, where is the noise correlation time. It is then shown with a numerical method that the Fokker-Planck equation relying on the assumption of local linearization bridges the exact limit for , and the standard one for =0. Some intriguing aspects of the short- region are discussed.

AB - The projection-operator method is used to find a Fokker-Planck equation with a time-dependent diffusion coefficient. It is shown that this equation is correct under a precise condition of small noise intensity and can be used successfully to study the problem of escape over the potential barrier of a bistable system. An exact expression for the first-passage time for , is found, where is the noise correlation time. It is then shown with a numerical method that the Fokker-Planck equation relying on the assumption of local linearization bridges the exact limit for , and the standard one for =0. Some intriguing aspects of the short- region are discussed.

UR - http://www.scopus.com/inward/record.url?scp=5544307462&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5544307462&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.38.3749

DO - 10.1103/PhysRevA.38.3749

M3 - Article

VL - 38

SP - 3749

EP - 3757

JO - Physical Review A

JF - Physical Review A

SN - 1050-2947

IS - 7

ER -