Nonlinear Response in the Driven Lattice Lorentz Gas

Leitmann, Sebastian; Franosch, Thomas

doi:10.1103/physrevlett.111.190603

Cited by 60 publications

(85 citation statements)

References 40 publications

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“…(14) and (15), and using the definition (10), one can explicitly obtain the TP velocity in the dilute limit, for arbitrary choice of jump probabilities and time scales τ, τ * . Notice that the comparison between the expression for V (F ) obtained in the dilute limit for unconfined geometries [44], following a computation analogous to that reported here, and the analytical result of [41], revealed that the decoupling approximation is indeed exact at lowest order in ρ, for arbitrary values of the time scales τ, τ * . We claim that this statement also holds for confined geometries.…”

Section: Linearized Solution In the Dilute Regimementioning

confidence: 99%

“…Recently, the behavior of V (F ) beyond the linear regime in lattice gas models has received great attention, triggered by the observation of the striking phenomenon of negative differential mobility (NDM), namely a nonmonotonic dependence of the TP velocity on the applied force [39][40][41][42][43][44][45]. Upon a gradual increase of the force F , the velocity grows linearly, as prescribed by the linear response, then approaches a maximal value and further decreases with an increase of F .…”

Section: Introductionmentioning

confidence: 99%

“…In this regime, remarkably, the differential mobility becomes negative. Moreover, we study in detail the behaviors arising from two specific choices of the TP jump probabilities, considered recently in [41,43,44], both satisfying the LDB, but differing in the explicit dependence on F in the directions orthogonal to the force. We derive the phase chart in the parameter space of the model where NDM is expected to occur for both kinds of jump probabilities.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Linearized Solution In the Dilute Regimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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“…The γ = 0 case corresponds to the driven lattice Lorentz gas and is known to show negative response irrespective of the choice of p, q [6,16,19]. The study of this system was started in the context of diffusion in random media with focus on the phase transition to a zero-current regime [19,20,21,22].…”

Section: Modelmentioning

confidence: 99%

“…Specific examples follow in the next sections. For broader physics background on the models and for previous work we also refer to [13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Mobility transition in a dynamic environment

Basu

Maes²

2014

J. Phys. A: Math. Theor.

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Abstract. Depending on how the dynamical activity of a particle in a random environment is influenced by an external field E, its differential mobility at intermediate E can turn negative. We discuss the case where for slowly changing random environment the driven particle shows negative differential mobility while that mobility turns positive for faster environment changes. We illustrate this transition using a 2D-lattice Lorentz model where a particle moves in a background of simple exclusion walkers. The effective escape rate of the particle (or minus its collision frequency) which is essential for its mobility-behavior depends both on E and on the kinetic rate γ of the exclusion walkers. Large γ, i.e., fast obstacle motion, amounts to merely rescaling the particle's free motion with the obstacle density, while slow obstacle dynamics results in particle motion that is more singularly related to its free motion and preserves the negative differential mobility already seen at γ = 0. In more general terms that we also illustrate using one-dimensional random walkers, the mobility transition is between the time-scales of the quasi-stationary regime and that of the fluid limit.

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Death and Resurrection of a Current by Disorder, Interaction or Periodic Driving

Demaerel

Maes

2018

J Stat Phys

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Because of disorder the current-field characteristic may show a first order phase transition as function of the field, at which the current jumps to zero when the driving exceeds a threshold. The discontinuity is caused by adding a finite correlation length in the disorder. At the same time the current may resurrect when the field is modulated in time, also discontinuously: a little shaking enables the current to jump up. Finally, in trapping models exclusion between particles postpones or even avoids the current from dying, while attraction may enhance it. We present simple models that illustrate those dynamical phase transitions in detail, and that allow full mathematical control.

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Nonlinear Response in the Driven Lattice Lorentz Gas

Cited by 60 publications

References 40 publications

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

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

Mobility transition in a dynamic environment

Death and Resurrection of a Current by Disorder, Interaction or Periodic Driving

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