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Dissimilar bouncy walkers

Lomholt, Michael A ; Lizana, Ludvig and Ambjörnsson, Tobias LU (2011) In Journal of Chemical Physics 134(4).
Abstract
We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants ξ(n), where n labels different bouncy walkers, are drawn from a distribution ϱ(ξ(n)). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when ϱ(ξ(n)) is heavy-tailed, ϱ(ξ(n))≃ξ(n) (-1-α) (0<α<1) for large ξ(n), we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q, t), follows a Mittag-Leffler relaxation, and the mean square displacement (MSD) of a tracer particle grows... (More)
We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants ξ(n), where n labels different bouncy walkers, are drawn from a distribution ϱ(ξ(n)). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when ϱ(ξ(n)) is heavy-tailed, ϱ(ξ(n))≃ξ(n) (-1-α) (0<α<1) for large ξ(n), we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q, t), follows a Mittag-Leffler relaxation, and the mean square displacement (MSD) of a tracer particle grows as t(δ) with time t, where δ = α∕(1 + α). If instead ϱ is light-tailed such that the mean friction constant exist, S(Q, t) decays exponentially and the MSD scales as t(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model. (Less)
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publication status
published
subject
in
Journal of Chemical Physics
volume
134
issue
4
article number
045101
publisher
American Institute of Physics (AIP)
external identifiers
  • wos:000286897600127
  • pmid:21280802
  • scopus:79551609552
  • pmid:21280802
ISSN
0021-9606
DOI
10.1063/1.3526941
language
English
LU publication?
yes
id
1773bf5b-9c69-4d50-8b1f-f4f4250e98ba (old id 1832507)
date added to LUP
2016-04-01 10:01:00
date last changed
2025-04-04 15:05:02
@article{1773bf5b-9c69-4d50-8b1f-f4f4250e98ba,
  abstract     = {{We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants ξ(n), where n labels different bouncy walkers, are drawn from a distribution ϱ(ξ(n)). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when ϱ(ξ(n)) is heavy-tailed, ϱ(ξ(n))≃ξ(n) (-1-α) (0&lt;α&lt;1) for large ξ(n), we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q, t), follows a Mittag-Leffler relaxation, and the mean square displacement (MSD) of a tracer particle grows as t(δ) with time t, where δ = α∕(1 + α). If instead ϱ is light-tailed such that the mean friction constant exist, S(Q, t) decays exponentially and the MSD scales as t(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model.}},
  author       = {{Lomholt, Michael A and Lizana, Ludvig and Ambjörnsson, Tobias}},
  issn         = {{0021-9606}},
  language     = {{eng}},
  number       = {{4}},
  publisher    = {{American Institute of Physics (AIP)}},
  series       = {{Journal of Chemical Physics}},
  title        = {{Dissimilar bouncy walkers}},
  url          = {{http://dx.doi.org/10.1063/1.3526941}},
  doi          = {{10.1063/1.3526941}},
  volume       = {{134}},
  year         = {{2011}},
}