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

Abstract. We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the Lévy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive CTRW, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long spatial tails and strong anomalous superdiffusion.

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“…(5), we first solve Eq. (14) in Fourier space and then we insert the result in Eq. (15), taking the limit of small k and ω.…”

Section: Solution Of the Master Equation For The Lévy Walkmentioning

confidence: 99%

Rare events and scaling properties in field-induced anomalous dynamics

Burioni¹,

Gradenigo²,

Sarracino³

et al. 2013

J. Stat. Mech.

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“…[24] it is shown that the position distribution converges to a Gaussian distribution. Its variance may however exhibit anomalous growth depending on the geometry [24][25][26]. In particular, for a quasi-1D narrow channel it has been shown that at large densities the position distribution of a tracer in a symmetric lattice gas converges to a Gaussian with variance ≃ t 3/2 , a strongly superdiffusive behavior.…”

Section: Introductionmentioning

confidence: 99%

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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“…In the linear response regime, a fundamental result is the fluctuationdissipation theorem, which relates system response and spontaneous fluctuations. Within the last years a great effort has been devoted to generalizations of this theorem to nonequilibrium situations [1][2][3][4], when the time reversal symmetry is broken, and also to elucidating the effects of the higher order contributions in the external perturbation [5][6][7][8][9][10][11]. From experimental perspective, theoretical understanding of the latter issues is of an utmost importance in several fields, such as active microrheology [12][13][14] and dynamics of nonequilibrium fluids [15,16].…”

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confidence: 99%

Microscopic Theory for Negative Differential Mobility in Crowded Environments

et al. 2014

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We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.PACS numbers: 05.40.Fb,83.10.Pp Introduction.-Quantifying the response of a complex system to an external force is one of the cornerstone problems of statistical mechanics. In the linear response regime, a fundamental result is the fluctuationdissipation theorem, which relates system response and spontaneous fluctuations. Within the last years a great effort has been devoted to generalizations of this theorem to nonequilibrium situations [1][2][3][4], when the time reversal symmetry is broken, and also to elucidating the effects of the higher order contributions in the external perturbation [5][6][7][8][9][10][11]. From experimental perspective, theoretical understanding of the latter issues is of an utmost importance in several fields, such as active microrheology [12][13][14] and dynamics of nonequilibrium fluids [15,16].A striking example of anomalous behavior beyond the linear regime is the negative response of a particle's velocity to an applied force, observed in diverse situations in which a particle subject to an external force F travels through a medium. The terminal drift velocity V (F ) attained by the driven particle is then a nonmonotonic function of the force: upon a gradual increase of F , the terminal drift velocity first grows as expected from linear response, reaches a peak value and eventually decreases. This means that the differential mobility of the driven particle becomes negative for F exceeding a certain threshold value. Such a counter-intuitive "getting more from pushing less" [17] behavior of the differential mobility (or of the differential conductivity) has been observed for a variety of physical systems and processes, e.g. for electron transfer in semiconductors at low temperatures [18][19][20][21], hopping processes in disordered media [22], transport of electrons in mixtures of atomic gases with reactive collisions [23], far-from-equilibrium quantum spin chains [24], some models of Brownian motors [25,26], soft matter colloidal particles [27], different nonequilibrium systems [17], and also for the kinetically constrained models of glass formers [28][29][30].Apart of these examples, negative differential mobility (NDM) has been observed in the minimal model of a driven lattice gas, which captures many essential features of the behavior in r...

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

Cited by 14 publications

References 23 publications

Rare events and scaling properties in field-induced anomalous dynamics

Rare events and scaling properties in field-induced anomalous dynamics

Driven tracers in narrow channels

Microscopic Theory for Negative Differential Mobility in Crowded Environments

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