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Single-file dynamics with different diffusion constants

Ambjörnsson, Tobias LU ; Lizana, Ludvig ; Lomholt, Michael A. and Silbey, Robert J. (2008) In The Journal of chemical physics 129(18).
Abstract
We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two-particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as... (More)
We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two-particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature. (Less)
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author
; ; and
publishing date
type
Contribution to journal
publication status
published
subject
in
The Journal of chemical physics
volume
129
issue
18
article number
185106
publisher
American Institute of Physics (AIP)
external identifiers
  • scopus:56349111134
ISSN
0021-9606
DOI
10.1063/1.3009853
language
English
LU publication?
no
id
4e4b6bb8-aa84-4890-b980-3f646955fb4e
date added to LUP
2019-05-03 11:31:37
date last changed
2022-04-02 08:28:46
@article{4e4b6bb8-aa84-4890-b980-3f646955fb4e,
  abstract     = {{We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two-particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.}},
  author       = {{Ambjörnsson, Tobias and Lizana, Ludvig and Lomholt, Michael A. and Silbey, Robert J.}},
  issn         = {{0021-9606}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{18}},
  publisher    = {{American Institute of Physics (AIP)}},
  series       = {{The Journal of chemical physics}},
  title        = {{Single-file dynamics with different diffusion constants}},
  url          = {{http://dx.doi.org/10.1063/1.3009853}},
  doi          = {{10.1063/1.3009853}},
  volume       = {{129}},
  year         = {{2008}},
}