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Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion

Sanders, Lloyd LU ; Lomholt, Michael A. ; Lizana, Ludvig ; Fogelmark, Karl LU ; Metzler, Ralf and Ambjörnsson, Tobias LU (2014) In New Journal of Physics 16.
Abstract
Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < x(2)(t)> similar or equal to t(alpha) of the mean squared displacement with 0 < alpha < 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < x(2)(t)> similar or equal to log(1/2)t with a universal 1/2... (More)
Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < x(2)(t)> similar or equal to t(alpha) of the mean squared displacement with 0 < alpha < 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < x(2)(t)> similar or equal to log(1/2)t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement < x(2)(t)> similar or equal to t(gamma) with 0 < gamma < 1/2, that is slower than the famed Harris law < x(2)(t)> similar or equal to t(1/2) without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process. (Less)
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author
; ; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
single-file diffusion, continuous time random walks, ageing
in
New Journal of Physics
volume
16
article number
113050
publisher
IOP Publishing
external identifiers
  • wos:000346764000002
  • scopus:84918799232
ISSN
1367-2630
DOI
10.1088/1367-2630/16/11/113050
language
English
LU publication?
yes
id
97ba5c4c-f59e-4726-9a8e-7e9babac7a2f (old id 4941467)
date added to LUP
2016-04-01 13:32:09
date last changed
2022-12-11 18:44:15
@article{97ba5c4c-f59e-4726-9a8e-7e9babac7a2f,
  abstract     = {{Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form &lt; x(2)(t)&gt; similar or equal to t(alpha) of the mean squared displacement with 0 &lt; alpha &lt; 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics &lt; x(2)(t)&gt; similar or equal to log(1/2)t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement &lt; x(2)(t)&gt; similar or equal to t(gamma) with 0 &lt; gamma &lt; 1/2, that is slower than the famed Harris law &lt; x(2)(t)&gt; similar or equal to t(1/2) without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.}},
  author       = {{Sanders, Lloyd and Lomholt, Michael A. and Lizana, Ludvig and Fogelmark, Karl and Metzler, Ralf and Ambjörnsson, Tobias}},
  issn         = {{1367-2630}},
  keywords     = {{single-file diffusion; continuous time random walks; ageing}},
  language     = {{eng}},
  publisher    = {{IOP Publishing}},
  series       = {{New Journal of Physics}},
  title        = {{Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion}},
  url          = {{http://dx.doi.org/10.1088/1367-2630/16/11/113050}},
  doi          = {{10.1088/1367-2630/16/11/113050}},
  volume       = {{16}},
  year         = {{2014}},
}