Velocity dependence of friction and Kramers relaxation rates

Gelin, M.F., and Kosov, D.S. (2007) Velocity dependence of friction and Kramers relaxation rates. Journal of Chemical Physics, 126 (24). 244501. pp. 1-5.

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Abstract

We study the influence of the velocity dependence of friction on the escape rate of a Brownian particle from the deep potential well (E(b)≫k(B)T, E(b) is the barrier height, k(B) is the Boltzmann constant, and T is the bath temperature). The bath-induced relaxation is treated within the Rayleigh model (a heavy particle of mass M in the bath of light particles of mass m≪M) up to the terms of the order of O(λ⁴), λ² = m/M≪1. The term ∼1 is equivalent to the Fokker-Planck dissipative operator, and the term ∼λ² is responsible for the velocity dependence of friction. As expected, the correction to the Kramers escape rate in the overdamped limit is proportional to λ²and is small. The corresponding correction in the underdamped limit is proportional to λ²E(b)/(k(B)T) and is not necessarily small. We thus suggest that the effects due to the velocity-dependent friction may be of considerable importance in determining the rate of escape of an under- and moderately damped Brownian particle from a deep potential well, while they are of minor importance for an overdamped particle.

Item ID: 26469
Item Type: Article (Research - C1)
ISSN: 1089-7690
Date Deposited: 20 Jun 2013 07:18
FoR Codes: 02 PHYSICAL SCIENCES > 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics > 020201 Atomic and Molecular Physics @ 50%
03 CHEMICAL SCIENCES > 0307 Theoretical and Computational Chemistry > 030704 Statistical Mechanics in Chemistry @ 50%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 100%
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