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Tracer particle diffusion in a system with hardcore interacting particles

Pigeon, Simon; Fogelmark, Karl LU ; Söderberg, Bo LU ; Mukhopadhyay, Gautam and Ambjörnsson, Tobias LU (2017) In Journal of Statistical Mechanics: Theory and Experiment 2017(12).
Abstract

In this study, inspired by the work of Nakazato and Kitahara (1980 Prog. Theor. Phys. 64 2261), we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on a regular Bravais lattice we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c.... (More)

In this study, inspired by the work of Nakazato and Kitahara (1980 Prog. Theor. Phys. 64 2261), we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on a regular Bravais lattice we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Brownian motion, correlation functions, diffusion, stochastic particle dynamics
in
Journal of Statistical Mechanics: Theory and Experiment
volume
2017
issue
12
publisher
IOP Publishing
external identifiers
  • scopus:85039779133
ISSN
1742-5468
DOI
10.1088/1742-5468/aa9db3
language
English
LU publication?
yes
id
aca055f9-d4fe-4a41-be4e-9526f6562d05
date added to LUP
2018-01-09 13:21:24
date last changed
2018-11-21 21:37:11
@article{aca055f9-d4fe-4a41-be4e-9526f6562d05,
  abstract     = {<p>In this study, inspired by the work of Nakazato and Kitahara (1980 Prog. Theor. Phys. 64 2261), we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on a regular Bravais lattice we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.</p>},
  articleno    = {123209},
  author       = {Pigeon, Simon and Fogelmark, Karl and Söderberg, Bo and Mukhopadhyay, Gautam and Ambjörnsson, Tobias},
  issn         = {1742-5468},
  keyword      = {Brownian motion,correlation functions,diffusion,stochastic particle dynamics},
  language     = {eng},
  month        = {12},
  number       = {12},
  publisher    = {IOP Publishing},
  series       = {Journal of Statistical Mechanics: Theory and Experiment},
  title        = {Tracer particle diffusion in a system with hardcore interacting particles},
  url          = {http://dx.doi.org/10.1088/1742-5468/aa9db3},
  volume       = {2017},
  year         = {2017},
}