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Universality and nonuniversality of mobility in heterogeneous single-file systems and Rouse chains

Lomholt, Michael A. and Ambjörnsson, Tobias LU (2014) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00 89(3).
Abstract
We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for nonequilibrium, heterogeneous, strongly interacting Brownian systems. The long time dynamics for such a single-file setup belongs to the same universality class as the Rouse model with dissimilar beads. The friction constants are drawn from a density rho(xi), and we derive an asymptotically exact solution for the mobility distribution P[mu(0)(s)], where mu(0)(s) is the Laplace-space mobility. If rho is light tailed (first moment exists), we find a self-averaging behavior: P[mu(0)(s)] = delta[mu(0)(s) - mu(s)], with mu(s) alpha s(1/2). When rho(xi) is heavy tailed, rho(xi) similar or equal to... (More)
We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for nonequilibrium, heterogeneous, strongly interacting Brownian systems. The long time dynamics for such a single-file setup belongs to the same universality class as the Rouse model with dissimilar beads. The friction constants are drawn from a density rho(xi), and we derive an asymptotically exact solution for the mobility distribution P[mu(0)(s)], where mu(0)(s) is the Laplace-space mobility. If rho is light tailed (first moment exists), we find a self-averaging behavior: P[mu(0)(s)] = delta[mu(0)(s) - mu(s)], with mu(s) alpha s(1/2). When rho(xi) is heavy tailed, rho(xi) similar or equal to xi(-1-alpha) (0 < alpha < 1) for large xi, we obtain moments <[mu(s)(0)(n)]> alpha s(beta n), where beta = 1/(1 + alpha) and there is no self-averaging. The results are corroborated by simulations. (Less)
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organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00
volume
89
issue
3
publisher
American Physical Society
external identifiers
  • wos:000332183000002
  • scopus:84898985358
ISSN
1539-3755
DOI
10.1103/PhysRevE.89.032101
language
English
LU publication?
yes
id
8744b389-c536-4804-addb-f27d0544cd71 (old id 4417574)
date added to LUP
2014-04-30 12:03:04
date last changed
2017-02-26 03:19:30
@article{8744b389-c536-4804-addb-f27d0544cd71,
  abstract     = {We study analytically the tracer particle mobility in single-file systems with distributed friction constants. Our system serves as a prototype for nonequilibrium, heterogeneous, strongly interacting Brownian systems. The long time dynamics for such a single-file setup belongs to the same universality class as the Rouse model with dissimilar beads. The friction constants are drawn from a density rho(xi), and we derive an asymptotically exact solution for the mobility distribution P[mu(0)(s)], where mu(0)(s) is the Laplace-space mobility. If rho is light tailed (first moment exists), we find a self-averaging behavior: P[mu(0)(s)] = delta[mu(0)(s) - mu(s)], with mu(s) alpha s(1/2). When rho(xi) is heavy tailed, rho(xi) similar or equal to xi(-1-alpha) (0 &lt; alpha &lt; 1) for large xi, we obtain moments &lt;[mu(s)(0)(n)]&gt; alpha s(beta n), where beta = 1/(1 + alpha) and there is no self-averaging. The results are corroborated by simulations.},
  articleno    = {032101},
  author       = {Lomholt, Michael A. and Ambjörnsson, Tobias},
  issn         = {1539-3755},
  language     = {eng},
  number       = {3},
  publisher    = {American Physical Society},
  series       = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)2001-01-01+01:002016-01-01+01:00},
  title        = {Universality and nonuniversality of mobility in heterogeneous single-file systems and Rouse chains},
  url          = {http://dx.doi.org/10.1103/PhysRevE.89.032101},
  volume       = {89},
  year         = {2014},
}