Two-state random walk model of diffusion. 2. Oscillatory diffusion

Balakrishnan, V. ; Venkataraman, G. (1981) Two-state random walk model of diffusion. 2. Oscillatory diffusion Pramana - Journal of Physics, 16 (6). pp. 437-455. ISSN 0304-4289

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Continuing our study of interrupted diffusion, we consider the problem of a particle executing a random walk interspersed with localized oscillations during its halts (e.g., at lattice sites). Earlier approaches proceedvia approximation schemes for the solution of the Fokker-Planck equation for diffusion in a periodic potential. In contrast, we visualize a two-state random walk in velocity space with the particle alternating between a state of flight and one of localized oscillation. Using simple, physically plausible inputs for the primary quantities characterising the random walk, we employ the powerful continuous-time random walk formalism to derive convenient and tractable closed-form expressions for all the objects of interest: the velocity autocorrelation, generalized diffusion constant, dynamic mobility, mean square displacement, dynamic structure factor (in the Gaussian approximation), etc. The interplay of the three characteristic times in the problem (the mean residence and flight times, and the period of the 'local mode') is elucidated. The emergence of a number of striking features of oscillatory diffusion (e.g., the local mode peak in the dynamic mobility and structure factor, and the transition between the oscillatory and diffusive regimes) is demonstrated.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Diffusion; Continuous-time Random Walk; Dynamic Mobility; Velocity Autocorrelation; Dynamic Structure Factor
ID Code:1051
Deposited On:25 Sep 2010 11:02
Last Modified:16 May 2016 12:13

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