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Foundation of fractional Langevin equation: Harmonization of a many-body problem

Lizana, Ludvig ; Ambjörnsson, Tobias LU ; Taloni, Alessandro ; Barkai, Eli and Lomholt, Michael A. (2010) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 81(5).
Abstract
In this study we derive a single-particle equation of motion, from first principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models and a relation derived by Kollmann.
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author
; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
volume
81
issue
5
publisher
American Physical Society
external identifiers
  • wos:000278148400028
  • scopus:77952338160
  • pmid:20866196
ISSN
1539-3755
DOI
10.1103/PhysRevE.81.051118
language
English
LU publication?
yes
id
f0f5f653-08be-4c65-a51e-ff64168d7f2f (old id 1616662)
date added to LUP
2016-04-01 10:19:01
date last changed
2024-04-07 06:56:51
@article{f0f5f653-08be-4c65-a51e-ff64168d7f2f,
  abstract     = {{In this study we derive a single-particle equation of motion, from first principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models and a relation derived by Kollmann.}},
  author       = {{Lizana, Ludvig and Ambjörnsson, Tobias and Taloni, Alessandro and Barkai, Eli and Lomholt, Michael A.}},
  issn         = {{1539-3755}},
  language     = {{eng}},
  number       = {{5}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)}},
  title        = {{Foundation of fractional Langevin equation: Harmonization of a many-body problem}},
  url          = {{http://dx.doi.org/10.1103/PhysRevE.81.051118}},
  doi          = {{10.1103/PhysRevE.81.051118}},
  volume       = {{81}},
  year         = {{2010}},
}