article · 29/03/2013
Fluctuations and correlations of a driven tracer in a hard-core lattice gas
Résumé
We consider a driven tracer particle (TP) in a bath of hard-core particles undergoing continuous exchanges with a reservoir. We develop an analytical framework which allows us to go beyond the standard force-velocity relation used for this minimal model of active microrheology and quantitatively analyze, for any density of the bath particles, the fluctuations of the TP position and their correlations with the occupation number of the bath particles. We obtain an exact Einstein-type relation which links these fluctuations in the absence of a driving force and the bath particles density profiles in the linear driving regime. For the one-dimensional case we also provide an approximate but very accurate explicit expression for the variance of the TP position and show that it can be a nonmonotonous function of the bath particles density: counterintuitively, an increase of the density may increase the dispersion of the TP position. We show that this nontrivial behavior, which could in principle be observed in active microrheology experiments, is induced by subtle cross correlations quantified by our approach. DOI: 10.1103/PhysRevE.87.032164
Citer cet article
Benichou, O., Illien, P., Oshanin, G., & Voituriez, R. (2013). Fluctuations and correlations of a driven tracer in a hard-core lattice gas. PHYSICAL REVIEW E, 87(3). https://doi.org/10.1103/PhysRevE.87.032164@article{Benichou2013_235,
author = {Benichou, O. and Illien, P. and Oshanin, G. and Voituriez, R.},
year = {2013},
month = {3},
title = {Fluctuations and correlations of a driven tracer in a hard-core lattice gas},
journal = {PHYSICAL REVIEW E},
volume = {87},
number = {3},
abstract = {We consider a driven tracer particle (TP) in a bath of hard-core particles undergoing continuous exchanges with a reservoir. We develop an analytical framework which allows us to go beyond the standard force-velocity relation used for this minimal model of active microrheology and quantitatively analyze, for any density of the bath particles, the fluctuations of the TP position and their correlations with the occupation number of the bath particles. We obtain an exact Einstein-type relation which links these fluctuations in the absence of a driving force and the bath particles density profiles in the linear driving regime. For the one-dimensional case we also provide an approximate but very accurate explicit expression for the variance of the TP position and show that it can be a nonmonotonous function of the bath particles density: counterintuitively, an increase of the density may increase the dispersion of the TP position. We show that this nontrivial behavior, which could in principle be observed in active microrheology experiments, is induced by subtle cross correlations quantified by our approach. DOI: 10.1103/PhysRevE.87.032164},
url = {http://www.dx.doi.org/10.1103/PhysRevE.87.032164},
doi = {10.1103/PhysRevE.87.032164},
issn = {1539-3755},
}TY - JOUR
AU - Benichou, O.
AU - Illien, P.
AU - Oshanin, G.
AU - Voituriez, R.
PY - 2013
DA - 2013/03/29
TI - Fluctuations and correlations of a driven tracer in a hard-core lattice gas
JO - PHYSICAL REVIEW E
VL - 87
IS - 3
SN - 1539-3755
AB - We consider a driven tracer particle (TP) in a bath of hard-core particles undergoing continuous exchanges with a reservoir. We develop an analytical framework which allows us to go beyond the standard force-velocity relation used for this minimal model of active microrheology and quantitatively analyze, for any density of the bath particles, the fluctuations of the TP position and their correlations with the occupation number of the bath particles. We obtain an exact Einstein-type relation which links these fluctuations in the absence of a driving force and the bath particles density profiles in the linear driving regime. For the one-dimensional case we also provide an approximate but very accurate explicit expression for the variance of the TP position and show that it can be a nonmonotonous function of the bath particles density: counterintuitively, an increase of the density may increase the dispersion of the TP position. We show that this nontrivial behavior, which could in principle be observed in active microrheology experiments, is induced by subtle cross correlations quantified by our approach. DOI: 10.1103/PhysRevE.87.032164
DO - 10.1103/PhysRevE.87.032164
UR - http://www.dx.doi.org/10.1103/PhysRevE.87.032164
ER -