Issue
EPL
Volume 81, Number 1, January 2008
Article Number 16003
Number of page(s) 6
Section Condensed Matter: Structural, Mechanical and Thermal Properties
DOI http://dx.doi.org/10.1209/0295-5075/81/16003
Published online 04 December 2007
EPL, 81 (2008) 16003
DOI: 10.1209/0295-5075/81/16003

Single-file diffusion of subdiffusive particles

T. Bandyopadhyay

Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre - Trombay, Mumbai 400 085, India


received 16 July 2007; accepted in final form 2 November 2007; published January 2008
published online 4 December 2007

Abstract
We introduce a fractional single-file diffusion (FSFD) model describing the stochastic evolution of an assembly of nonpassing particles (single-file (SF) system), where in addition to the excluded-volume interaction between the particles, they individually follow sticky trajectories (fractional diffusion (FD)) on a fractal support. While the long-range correlations between the particles mediated through the former interaction is treated through the reflection principle, the sticky trajectories involve fractional time derivatives whose order is distributed over the interval from zero to one. A detailed study of the propagators of FSFD is made and compared with the normal SF diffusion through their time evolution in state space. Both the diffusion mechanisms, SF and FD, are known for anomalous subdiffusive behaviour; their combined entity, FSFD has been found to exhibit further anomality leading to ultraslow diffusion. Through an integral transformation of the Gaussian propagator, a generalised expression for the mean square displacement of a tagged particle undergoing FSFD is obtained.

PACS
66.30.Pa - Diffusion in nanoscale solids.
47.53.+n - Fractals in fluid dynamics.
02.50.Ey - Stochastic processes.

© EPLA 2008