Diffusion on a rugged energy landscape with spatial correlations

作者：Banerjee Saikat^*; Biswas Rajib; Seki Kazuhiko; Bagchi Biman

来源：Journal of Chemical Physics, 2014, 141(12): 124105.

DOI：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%26apos;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 %26quot;three-site traps%26quot; (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%26apos;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 %26gt;%26gt; k(B)T) gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids.

• 出版日期2014-9-28