Two-state random walk model of diffusion. 2. Oscillatory diffusion |
| |
Authors: | V Balakrishnan G Venkataraman |
| |
Institution: | (1) Department of Physics, Indian Institute of Technology, 600 036 Madras, India;(2) Reactor Research Centre, 603 102 Kalpakkam, Tamil Nadu, India |
| |
Abstract: | 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. |
| |
Keywords: | Diffusion continuous-time random walk dynamic mobility velocity autocorrelation dynamic structure factor |
本文献已被 SpringerLink 等数据库收录! |
|