Two-state random walk model of lattice diffusion. 1. Self-correlation function

Balakrishnan, V. ; Venkataraman, G. (1981) Two-state random walk model of lattice diffusion. 1. Self-correlation function Pramana - Journal of Physics, 16 (2). pp. 109-130. ISSN 0304-4289

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Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (ind dimensions, and with arbitrary directional bias) for temporally uncorrelated jump diffusion and for the 'fluid diffusion' counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for 'oscillatory diffusion' are taken up in part 2.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Diffusion; Self-Correlation Function; Continuous-Time Random Walk Theory; Two-State Random Walk; Renewal Process
ID Code:1053
Deposited On:25 Sep 2010 11:09
Last Modified:16 May 2016 12:13

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