### Abstract

Accuracy of the Kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. Disagreement between the Kramers rate and the dynamical one is shown to reach 15% in the cases when much better agreement is expected. Corrections to the Kramers formulas accounting for the higher derivatives of the potential are obtained. The small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential. The distance between the potential barrier and the absorptive border is accounted for as well. This corrected Kramers rate is demonstrated to agree with the dynamical rate typically within 2%. Probably the most interesting result is that despite the corrections are derived in the case of the overdamped Brownian motion, the above 2% agreement holds even in the case of medium friction.

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

Pages (from-to) | 6084-6100 |

Number of pages | 17 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 391 |

Issue number | 23 |

DOIs | |

Publication status | Published - 1 Dec 2012 |

### Fingerprint

### Keywords

- Corrections to Kramers formulas
- Decay rate
- Kramers rate
- Metastable system

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistics and Probability

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*391*(23), 6084-6100. https://doi.org/10.1016/j.physa.2012.06.064

**Modified Kramers formulas for the decay rate in agreement with dynamical modeling.** / Pavlova, E. G.; Aktaev, N. E.; Gontchar, I. I.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 391, no. 23, pp. 6084-6100. https://doi.org/10.1016/j.physa.2012.06.064

}

TY - JOUR

T1 - Modified Kramers formulas for the decay rate in agreement with dynamical modeling

AU - Pavlova, E. G.

AU - Aktaev, N. E.

AU - Gontchar, I. I.

PY - 2012/12/1

Y1 - 2012/12/1

N2 - Accuracy of the Kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. Disagreement between the Kramers rate and the dynamical one is shown to reach 15% in the cases when much better agreement is expected. Corrections to the Kramers formulas accounting for the higher derivatives of the potential are obtained. The small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential. The distance between the potential barrier and the absorptive border is accounted for as well. This corrected Kramers rate is demonstrated to agree with the dynamical rate typically within 2%. Probably the most interesting result is that despite the corrections are derived in the case of the overdamped Brownian motion, the above 2% agreement holds even in the case of medium friction.

AB - Accuracy of the Kramers approximate formulas for the thermal decay rate of the metastable state is studied for the anharmonic shapes of the potential pocket and the barrier. This is done by the comparison with the quasistationary rate resulting from the dynamical modeling. Disagreement between the Kramers rate and the dynamical one is shown to reach 15% in the cases when much better agreement is expected. Corrections to the Kramers formulas accounting for the higher derivatives of the potential are obtained. The small parameters are the ratios of the thermal energy to the stiffnesses at the extremes of the potential. The distance between the potential barrier and the absorptive border is accounted for as well. This corrected Kramers rate is demonstrated to agree with the dynamical rate typically within 2%. Probably the most interesting result is that despite the corrections are derived in the case of the overdamped Brownian motion, the above 2% agreement holds even in the case of medium friction.

KW - Corrections to Kramers formulas

KW - Decay rate

KW - Kramers rate

KW - Metastable system

UR - http://www.scopus.com/inward/record.url?scp=84865705410&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865705410&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2012.06.064

DO - 10.1016/j.physa.2012.06.064

M3 - Article

VL - 391

SP - 6084

EP - 6100

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 23

ER -