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Rate processes with dynamical disorder: A direct variational approach

Debnath, Ananya and Chakrabarti, Rajarshi and Sebastian, KL (2006) Rate processes with dynamical disorder: A direct variational approach. In: Journal Of Chemical Physics, 124 (20). 204111-1-204111-.

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Using path integral approach, we develop variational approximations to the calculation of survival probability for rate processes with dynamical disorder. We derive both upper and lower bounds to the survival probability using Jensen's inequality. The inequalities involve the use of a trial action for which the path integrals can be evaluated exactly. Any parameter in the trial action can be varied to optimize the bounds. We have also derived a lower bound to the rate of the process. As a simple illustration, we apply the method to the problem of a particle undergoing Brownian motion in a harmonic potential well, in the presence of a delta function sink, for which one can calculate the exact survival probability numerically. The calculation confirms the two inequalities. The method should be very useful in similar but more complex problems where even numerical solution is not possible.

Item Type: Journal Article
Publication: Journal Of Chemical Physics
Publisher: American Institute Of Physics
Additional Information: Copyright of this article belongs to American Institute Of Physics.
Keywords: reaction kinetics theory;reaction rate constants;variational techniques;probability;Brownian motion.
Department/Centre: Division of Chemical Sciences > Inorganic & Physical Chemistry
Date Deposited: 08 Apr 2009 05:28
Last Modified: 19 Sep 2010 04:58
URI: http://eprints.iisc.ac.in/id/eprint/17785

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