Corrections to Kramers formula describing the decay rate of a metastable state

N. E. Aktaev, K. A. Bannova

Research output: Contribution to journal › Article

Abstract

The work investigates the accuracy of the Kramers approximate formula describing the decay rate of a metastable state. The study was performed by comparing the rate obtained through Kramers formula with the quasistationary rate derived by dynamical modeling that was performed by solving the Langevin equation. We have demonstrated that the non-correlation between Kramers rate and dynamical rate reached 15%, while a better correlation was expected. The study allowed us to generate corrections to Kramers formula by accounting for the higher derivatives of the potential. The rate obtained by the corrected formula exhibits the correlation with the dynamic rate of better than 1%.

Original language	English
Pages (from-to)	128-132
Number of pages	5
Journal	Key Engineering Materials
Volume	685
DOIs	https://doi.org/10.4028/www.scientific.net/KEM.685.128
Publication status	Published - 2016
Event	4th International Conference for Young Scientists High Technology: Research and Applications, HTRA 2015 - Tomsk, Russian Federation Duration: 21 Apr 2015 → 24 Apr 2015

Fingerprint

Keywords

Dynamical modeling
Kramers formula
Kramers rate
Metastable state
Quasistationary rate

ASJC Scopus subject areas

Materials Science(all)
Mechanics of Materials
Mechanical Engineering

Cite this

Aktaev, N. E., & Bannova, K. A. (2016). Corrections to Kramers formula describing the decay rate of a metastable state. Key Engineering Materials, 685, 128-132. https://doi.org/10.4028/www.scientific.net/KEM.685.128

@article{56199600416d4b6fab2a54383cb9a99d,

title = "Corrections to Kramers formula describing the decay rate of a metastable state",

abstract = "The work investigates the accuracy of the Kramers approximate formula describing the decay rate of a metastable state. The study was performed by comparing the rate obtained through Kramers formula with the quasistationary rate derived by dynamical modeling that was performed by solving the Langevin equation. We have demonstrated that the non-correlation between Kramers rate and dynamical rate reached 15{\%}, while a better correlation was expected. The study allowed us to generate corrections to Kramers formula by accounting for the higher derivatives of the potential. The rate obtained by the corrected formula exhibits the correlation with the dynamic rate of better than 1{\%}.",

keywords = "Dynamical modeling, Kramers formula, Kramers rate, Metastable state, Quasistationary rate",

author = "Aktaev, {N. E.} and Bannova, {K. A.}",

year = "2016",

doi = "10.4028/www.scientific.net/KEM.685.128",

language = "English",

volume = "685",

pages = "128--132",

journal = "Key Engineering Materials",

issn = "1013-9826",

publisher = "Trans Tech Publications",

note = "4th International Conference for Young Scientists High Technology: Research and Applications, HTRA 2015 ; Conference date: 21-04-2015 Through 24-04-2015",

}

TY - JOUR

T1 - Corrections to Kramers formula describing the decay rate of a metastable state

AU - Aktaev, N. E.

AU - Bannova, K. A.

PY - 2016

Y1 - 2016

N2 - The work investigates the accuracy of the Kramers approximate formula describing the decay rate of a metastable state. The study was performed by comparing the rate obtained through Kramers formula with the quasistationary rate derived by dynamical modeling that was performed by solving the Langevin equation. We have demonstrated that the non-correlation between Kramers rate and dynamical rate reached 15%, while a better correlation was expected. The study allowed us to generate corrections to Kramers formula by accounting for the higher derivatives of the potential. The rate obtained by the corrected formula exhibits the correlation with the dynamic rate of better than 1%.

AB - The work investigates the accuracy of the Kramers approximate formula describing the decay rate of a metastable state. The study was performed by comparing the rate obtained through Kramers formula with the quasistationary rate derived by dynamical modeling that was performed by solving the Langevin equation. We have demonstrated that the non-correlation between Kramers rate and dynamical rate reached 15%, while a better correlation was expected. The study allowed us to generate corrections to Kramers formula by accounting for the higher derivatives of the potential. The rate obtained by the corrected formula exhibits the correlation with the dynamic rate of better than 1%.

KW - Dynamical modeling

KW - Kramers formula

KW - Kramers rate

KW - Metastable state

KW - Quasistationary rate

UR - http://www.scopus.com/inward/record.url?scp=84958213130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958213130&partnerID=8YFLogxK

U2 - 10.4028/www.scientific.net/KEM.685.128

DO - 10.4028/www.scientific.net/KEM.685.128

M3 - Article

AN - SCOPUS:84958213130

VL - 685

SP - 128

EP - 132

JO - Key Engineering Materials

JF - Key Engineering Materials

SN - 1013-9826

T2 - 4th International Conference for Young Scientists High Technology: Research and Applications, HTRA 2015

Y2 - 21 April 2015 through 24 April 2015

ER -

Access to Document

10.4028/www.scientific.net/KEM.685.128