Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

Burlatsky, S. F.; Oshanin, Gleb; Moreau, M.; Reinhardt, William P.

doi:10.1103/physreve.54.3165

Cited by 73 publications

(134 citation statements)

References 38 publications

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“…The q = 0 term however only leads to a constant in the final expression of G r|r ′ , which has already been accounted for in Eq. (14). We therefore use the conventioñ G 0|r ′ = 0 in the following.…”

Section: Solution Of the Discrete System For A Finite Channel Widthmentioning

confidence: 99%

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Driven tracers in narrow channels

2017

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Steady state properties of a driven tracer moving in a narrow two dimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a one dimensional SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of mean field theory and exact solution in the limit where no exchange is allowed, gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.

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Section: Solution Of the Discrete System For A Finite Channel Widthmentioning

confidence: 99%

“…In addition, the bath particles may also undergo nonconserving adsorption-desorption processes. Infinite 1D [13][14][15][16], 2D [17,18], 3D spaces [19] and even comb-like geometries [20] have been analyzed. In a similar setup a tracer moving with a constant velocity has been studied in 2D using an Ising-like model [27].…”

Section: Introductionmentioning

confidence: 99%

Driven tracers in narrow channels

2017

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“…Last, in the case of a constant external forcing experienced by all the particles, it identifies with the asymmetric exclusion process, which has now become a paradigmatic model, both in the absence (see [14] for a recent review) or in the presence [15] of adsorption/desorption processes. This model of driven tracer diffusion has been investigated both in the physical [16][17][18][19][20] and in the mathematical [21,22] literatures. Most of the obtained results, including proofs of the Einstein relation, are limited to the large time behavior of the mean position X tr of the tracer particle and the stationary density profiles of the bath η r , where η r stands for the occupation number of the site r of the lattice, equal to 1 if occupied by a bath particle and 0 otherwise.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations and correlations of a driven tracer in a hard-core lattice gas

et al. 2013

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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 non-monotoneous function of the bath particles density: counter-intuitively, an increase of the density may increase the dispersion of the TP position. We show that this non trivial behavior, which could in principle be observed in active microrheology experiments, is induced by subtle cross-correlations quantified by our approach.

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“…On the one hand, in [59] the computation of the density profiles around a TP in an adsorbed monolayer of hard-core particles showed that, if the particle density in the monolayer is conserved, the approach to the equilibrium density with the distance past the tracer is described by a power-law function [61]. On the other hand, it is known [58,62] that in strictly one-dimensional systems -the so-called singlefiles, there are no stationary profiles past the driven tracer. The systems we consider here are physically two-(stripes) and three-dimensional (capillaries), but effectively they are quasi-one-dimensional since they are of an infinite extent only in one direction.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments

et al. 2016

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We study analytically the dynamics and the micro-structural changes of a host medium caused by a driven tracer particle moving in a confined, quiescent molecular crowding environment. Imitating typical settings of active micro-rheology experiments, we consider here a minimal model comprising a geometrically confined lattice system -a two-dimensional strip-like or a three-dimensional capillarylike -populated by two types of hard-core particles with stochastic dynamics -a tracer particle driven by a constant external force and bath particles moving completely at random. Resorting to a decoupling scheme, which permits us to go beyond the linear-response approximation (Stokes regime) for arbitrary densities of the lattice gas particles, we determine the force-velocity relation for the tracer particle and the stationary density profiles of the host medium particles around it. These results are validated a posteriori by extensive numerical simulations for a wide range of parameters. Our theoretical analysis reveals two striking features: a) We show that, under certain conditions, the terminal velocity of the driven tracer particle is a nonmonotonic function of the force, so that in some parameter range the differential mobility becomes negative, and b) the biased particle drives the whole system into a nonequilibrium steady-state with a stationary particle density profile past the tracer, which decays exponentially, in sharp contrast with the behavior observed for unbounded lattices, where an algebraic decay is known to take place.

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Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

Abstract: Dynamics of a tracer particle subject to a constant driving force E in a onedimensional lattice gas of hard-core particles whose transition rates are symmetric. We show that the mean displacement of the driven tracer, X T (E, t),

Cited by 73 publications

References 38 publications

Driven tracers in narrow channels

Driven tracers in narrow channels

Fluctuations and correlations of a driven tracer in a hard-core lattice gas

Nonlinear response and emerging nonequilibrium microstructures for biased diffusion in confined crowded environments

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