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Ageing single file motion

Metzler, R.; Sanders, Lloyd LU ; Lomholt, M. A.; Lizana, L.; Fogelmark, Karl LU and Ambjörnsson, Tobias LU (2014) In The European Physical Journal. Special Topics 223(14). p.3287-3293
Abstract
The mean squared displacement of a tracer particle in a single file of identical particles with excluded volume interactions shows the famed Harris scaling aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (1/2) t (1/2) as function of time. Here we study what happens to this law when each particle of the single file interacts with the environment such that it is transiently immobilised for times tau with a power-law distribution psi(tau) a parts per thousand integral (tau(a similar to...))(alpha), and different ranges of the exponent alpha are considered. We find a dramatic slow-down of the motion of a tracer particle from Harris' law to an ultraslow, logarithmic time evolution aEurox (2)(t)aEuro parts per thousand a... (More)
The mean squared displacement of a tracer particle in a single file of identical particles with excluded volume interactions shows the famed Harris scaling aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (1/2) t (1/2) as function of time. Here we study what happens to this law when each particle of the single file interacts with the environment such that it is transiently immobilised for times tau with a power-law distribution psi(tau) a parts per thousand integral (tau(a similar to...))(alpha), and different ranges of the exponent alpha are considered. We find a dramatic slow-down of the motion of a tracer particle from Harris' law to an ultraslow, logarithmic time evolution aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (0) log (1/2)(t) when 0 < alpha < 1. In the intermediate case 1 < alpha < 2, we observe a power-law form for the mean squared displacement, with a modified scaling exponent as compared to Harris' law. Once alpha is larger than two, the Brownian single file behaviour and thus Harris' law are restored. We also point out that this process is weakly non-ergodic in the sense that the time and ensemble averaged mean squared displacements are disparate. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
The European Physical Journal. Special Topics
volume
223
issue
14
pages
3287 - 3293
publisher
EDP Sciences
external identifiers
  • wos:000346416400018
  • scopus:84918528100
ISSN
1951-6355
DOI
10.1140/epjst/e2014-02333-5
language
English
LU publication?
yes
id
5b5e1158-7ef3-4fba-966d-530ef7e9d8e7 (old id 4944660)
date added to LUP
2015-01-28 11:49:44
date last changed
2017-04-09 04:00:53
@article{5b5e1158-7ef3-4fba-966d-530ef7e9d8e7,
  abstract     = {The mean squared displacement of a tracer particle in a single file of identical particles with excluded volume interactions shows the famed Harris scaling aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (1/2) t (1/2) as function of time. Here we study what happens to this law when each particle of the single file interacts with the environment such that it is transiently immobilised for times tau with a power-law distribution psi(tau) a parts per thousand integral (tau(a similar to...))(alpha), and different ranges of the exponent alpha are considered. We find a dramatic slow-down of the motion of a tracer particle from Harris' law to an ultraslow, logarithmic time evolution aEurox (2)(t)aEuro parts per thousand a parts per thousand integral K (0) log (1/2)(t) when 0 &lt; alpha &lt; 1. In the intermediate case 1 &lt; alpha &lt; 2, we observe a power-law form for the mean squared displacement, with a modified scaling exponent as compared to Harris' law. Once alpha is larger than two, the Brownian single file behaviour and thus Harris' law are restored. We also point out that this process is weakly non-ergodic in the sense that the time and ensemble averaged mean squared displacements are disparate.},
  author       = {Metzler, R. and Sanders, Lloyd and Lomholt, M. A. and Lizana, L. and Fogelmark, Karl and Ambjörnsson, Tobias},
  issn         = {1951-6355},
  language     = {eng},
  number       = {14},
  pages        = {3287--3293},
  publisher    = {EDP Sciences},
  series       = {The European Physical Journal. Special Topics},
  title        = {Ageing single file motion},
  url          = {http://dx.doi.org/10.1140/epjst/e2014-02333-5},
  volume       = {223},
  year         = {2014},
}