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Diffusion on a rugged energy landscape with spatial correlations

Banerjee, Saikat and Biswas, Rajib and Seki, Kazuhiko and Bagchi, Biman (2014) Diffusion on a rugged energy landscape with spatial correlations. In: JOURNAL OF CHEMICAL PHYSICS, 141 (12).

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Official URL: http://dx.doi.org/ 10.1063/1.4895905


Rugged energy landscapes find wide applications in diverse fields ranging from astrophysics to protein folding. We study the dependence of diffusion coefficient (D) of a Brownian particle on the distribution width (epsilon) of randomness in a Gaussian random landscape by simulations and theoretical analysis. We first show that the elegant expression of Zwanzig Proc. Natl. Acad. Sci. U.S.A. 85, 2029 (1988)] for D(epsilon) can be reproduced exactly by using the Rosenfeld diffusion-entropy scaling relation. Our simulations show that Zwanzig's expression overestimates D in an uncorrelated Gaussian random lattice - differing by almost an order of magnitude at moderately high ruggedness. The disparity originates from the presence of ``three-site traps'' (TST) on the landscape - which are formed by the presence of deep minima flanked by high barriers on either side. Using mean first passage time formalism, we derive a general expression for the effective diffusion coefficient in the presence of TST, that quantitatively reproduces the simulation results and which reduces to Zwanzig's form only in the limit of infinite spatial correlation. We construct a continuous Gaussian field with inherent correlation to establish the effect of spatial correlation on random walk. The presence of TSTs at large ruggedness (epsilon >> k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. (C) 2014 AIP Publishing LLC.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the AMER INST PHYSICS, CIRCULATION & FULFILLMENT DIV, 2 HUNTINGTON QUADRANGLE, STE 1 N O 1, MELVILLE, NY 11747-4501 USA
Department/Centre: Division of Chemical Sciences > Solid State & Structural Chemistry Unit
Date Deposited: 14 Nov 2014 07:28
Last Modified: 14 Nov 2014 07:28
URI: http://eprints.iisc.ac.in/id/eprint/50268

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