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Metastable transitions in inertial Langevin systems: What can be different from the overdamped case?

Part of: Statistical mechanics, structure of matter Stochastic analysis

Published online by Cambridge University Press:  19 September 2018

ANDRE N. SOUZA  and
MOLEI TAO
ANDRE N. SOUZA
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA emails: andre.souza@gatech.edu; mtao@gatech.edu
MOLEI TAO
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, USA emails: andre.souza@gatech.edu; mtao@gatech.edu
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Abstract

Metastable transitions in Langevin dynamics can exhibit rich behaviours that are markedly different from its overdamped limit. In addition to local alterations of the transition path geometry, more fundamental global changes may exist. For instance, when the dissipation is weak, heteroclinic connections that exist in the overdamped limit do not necessarily have a counterpart in the Langevin system, potentially leading to different transition rates. Furthermore, when the friction coefficient depends on the velocity, the overdamped limit no longer exists, but it is still possible to efficiently find instantons. The approach, we employed for these discoveries, was based on (i) a simple rewriting of the Freidlin–Wentzell action in terms of time-reversed dynamics and (ii) an adaptation of the string method, which was originally designed for gradient systems, to this specific non-gradient system.

Keywords

Freidlin–Wentzell large deviation theoryinstantoninertial Langevin equationunderdamped dynamicsmatrix-valued variable friction coefficient

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 82-08: Computational methods
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Special Issue 5: Stochastic Analysis in Applications , October 2019 , pp. 830 - 852
Copyright
© Cambridge University Press 2018 

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Footnotes

†

M. T. is partially supported by NSF grant DMS-1521667 and ECCS-1829821 and A. S. is partially supported by DMS-1344199.

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