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A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space

Chakrabarti, Rajarshi and Sebastian, KL (2009) A lower bound to the survival probability and an approximate first passage time distribution for Markovian and non-Markovian dynamics in phase space. In: Journal of chemical physics, 131 (22).

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Abstract

We derive a very general expression of the survival probability and the first passage time distribution for a particle executing Brownian motion in full phase space with an absorbing boundary condition at a point in the position space, which is valid irrespective of the statistical nature of the dynamics. The expression, together with the Jensen's inequality, naturally leads to a lower bound to the actual survival probability and an approximate first passage time distribution. These are expressed in terms of the position-position, velocity-velocity, and position-velocity variances. Knowledge of these variances enables one to compute a lower bound to the survival probability and consequently the first passage distribution function. As examples, we compute these for a Gaussian Markovian process and, in the case of non-Markovian process, with an exponentially decaying friction kernel and also with a power law friction kernel. Our analysis shows that the survival probability decays exponentially at the long time irrespective of the nature of the dynamics with an exponent equal to the transition state rate constant.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to American Institute of Physics.
Keywords: Brownian motion; Gaussian processes; Markov processes; probability
Department/Centre: Division of Chemical Sciences > Inorganic & Physical Chemistry
Depositing User: Id for Latest eprints
Date Deposited: 12 Jan 2010 09:18
Last Modified: 19 Sep 2010 05:54
URI: http://eprints.iisc.ac.in/id/eprint/25370

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