article · 01/11/2015
Distribution of the position of a driven tracer in a hardcore lattice gas
Résumé
We study the position of a biased tracer particle (TP) in a bath of hardcore particles moving on a lattice of arbitrary dimension and in contact with a reservoir. Starting from the master equation satisfied by the joint probability of the TP position and the bath configuration and resorting to a mean-field-type approximation, we presented a computation of the fluctuations of the TP position in a previous publication (Benichou et al 2013 Phys. Rev. E 87 032164). Counter-intuitively, on a one-dimensional lattice, the diffusion coefficient of the TP was shown to be a nonmonotonic function of the density of bath particles, and reaches a maximum for a nonzero value of the density. Here, we (i) give the details of this computation and offer a physical insight into the understanding of the nonmonotonicity of the diffusion coefficient; (ii) extend the mean-field-type approximation to decouple higher-order correlation functions, and obtain the evolution equation satisfied by the cumulant generating function of the position of the TP, valid in any space dimension. In the particular case of a one-dimensional lattice, we solve this equation and obtain the probability distribution of the TP position. We show that the position rescaled by its fluctuations is asymptotically distributed according to a Gaussian distribution in the long-time limit.
Citer cet article
Illien, P., Benichou, O., Oshanin, G., & Voituriez, R. (2015). Distribution of the position of a driven tracer in a hardcore lattice gas. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT. https://doi.org/10.1088/1742-5468/2015/11/P11016@article{Illien2015_190,
author = {Illien, Pierre and Benichou, Olivier and Oshanin, Gleb and Voituriez, Raphael},
year = {2015},
month = {11},
title = {Distribution of the position of a driven tracer in a hardcore lattice gas},
journal = {JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT},
number = {P11016},
abstract = {We study the position of a biased tracer particle (TP) in a bath of hardcore particles moving on a lattice of arbitrary dimension and in contact with a reservoir. Starting from the master equation satisfied by the joint probability of the TP position and the bath configuration and resorting to a mean-field-type approximation, we presented a computation of the fluctuations of the TP position in a previous publication (Benichou et al 2013 Phys. Rev. E 87 032164). Counter-intuitively, on a one-dimensional lattice, the diffusion coefficient of the TP was shown to be a nonmonotonic function of the density of bath particles, and reaches a maximum for a nonzero value of the density. Here, we (i) give the details of this computation and offer a physical insight into the understanding of the nonmonotonicity of the diffusion coefficient; (ii) extend the mean-field-type approximation to decouple higher-order correlation functions, and obtain the evolution equation satisfied by the cumulant generating function of the position of the TP, valid in any space dimension. In the particular case of a one-dimensional lattice, we solve this equation and obtain the probability distribution of the TP position. We show that the position rescaled by its fluctuations is asymptotically distributed according to a Gaussian distribution in the long-time limit.},
url = {http://www.dx.doi.org/10.1088/1742-5468/2015/11/P11016},
doi = {10.1088/1742-5468/2015/11/P11016},
issn = {1742-5468},
}TY - JOUR
AU - Illien, Pierre
AU - Benichou, Olivier
AU - Oshanin, Gleb
AU - Voituriez, Raphael
PY - 2015
DA - 2015/11/01
TI - Distribution of the position of a driven tracer in a hardcore lattice gas
JO - JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
IS - P11016
SN - 1742-5468
AB - We study the position of a biased tracer particle (TP) in a bath of hardcore particles moving on a lattice of arbitrary dimension and in contact with a reservoir. Starting from the master equation satisfied by the joint probability of the TP position and the bath configuration and resorting to a mean-field-type approximation, we presented a computation of the fluctuations of the TP position in a previous publication (Benichou et al 2013 Phys. Rev. E 87 032164). Counter-intuitively, on a one-dimensional lattice, the diffusion coefficient of the TP was shown to be a nonmonotonic function of the density of bath particles, and reaches a maximum for a nonzero value of the density. Here, we (i) give the details of this computation and offer a physical insight into the understanding of the nonmonotonicity of the diffusion coefficient; (ii) extend the mean-field-type approximation to decouple higher-order correlation functions, and obtain the evolution equation satisfied by the cumulant generating function of the position of the TP, valid in any space dimension. In the particular case of a one-dimensional lattice, we solve this equation and obtain the probability distribution of the TP position. We show that the position rescaled by its fluctuations is asymptotically distributed according to a Gaussian distribution in the long-time limit.
DO - 10.1088/1742-5468/2015/11/P11016
UR - http://www.dx.doi.org/10.1088/1742-5468/2015/11/P11016
ER -