Diffusion of tagged particle in an exclusion process
Name
APS MIT Open Access Policy Agreement final 12 07 09.pdf
Size
224.45 KB
Format
Adobe PDF
Checksum (MD5)
badb9e5545b14c85bafef7a29d5cb053
Author(s)
Silbey, Robert J.
Barkai, E.
Date Issued
April 2010
Journal
Physical Review E
Publisher
American Physical Society
Citation
Barkai, E., and R. Silbey. “Diffusion of tagged particle in an exclusion process.” Physical Review E 81.4 (2010): 041129. © 2010 The American Physical Society.
Version
Final published version
Abstract
We study the diffusion of tagged hard-core interacting Brownian point particles under the influence of an
external force field in one dimension. Using the Jepsen line we map this many-particle problem onto a single
particle one. We obtain general equations for the distribution and the mean-square displacement {(xT)[superscript 2]} of the tagged center particle valid for rather general external force fields and initial conditions. The case of symmetric distribution of initial conditions around the initial position of the tagged particle on x=0 and symmetric
potential fields V(x)=V(−x) yields zero drift {xT}=0 and is investigated in detail. We find {(xT)superscript 2]}=R(1−R)/2Nr[superscript 2] where 2N is the (large) number of particles in the system. R is a single particle reflection coefficient,i.e., the probability that a particle free of collisions starts on x[subscript 0]>0 and remains in x>0 while r is theprobability density of noninteracting particles on the origin. We show that this equation is related to themathematical theory of order statistics and it can be used to find {(xT)[superscript 2]} even when the motion betweencollision events is not Brownian (e.g., it might be ballistic or anomalous diffusion). As an example we derive the Percus relation for non-Gaussian diffusion. A wide range of physical behaviors emerge which are very
different than the classical single file subdiffusion {(xT)[superscript 2]}~t[superscript 1/2] found for uniformly distributed particles in an infinite space and in the absence of force fields.
MIT Department
Massachusetts Institute of Technology. Department of Chemistry
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevE.81.041129
