Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas

Leitmann, Sebastian; Schwab, Thomas; Franosch, Thomas

doi:10.1103/physreve.97.022101

Cited by 5 publications

(7 citation statements)

References 62 publications

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“…In the new basis, solving equation (26) reduces to inverting a 3 × 3 matrix problem in the subspace spanned by |p x , |d x 2 , and |s . With the help of the symmetry considerations, the three-dimensional lattice Lorentz problem is of the same complexity as its two-dimensional analogue [21], and can be implemented efficiently by computer algebra.…”

Section: Calculation Of the Forward-scattering Amplitudementioning

confidence: 99%

“…With this representation, we can follow the approach outlined in [21] for the square lattice. We express the dynamics of the tracer particle in the presence of obstacles in terms of the propagator Ĝ witĥ…”

Section: Obstacle Obstructed Motionmentioning

confidence: 99%

“…There has been recent progress on the driven lattice Lorentz system in two dimensions, where the equilibrium dynamics in first order of the density [16][17][18] has been generalized to an exact analytic solution for the case of a force pulling on the tracer particle [19][20][21]. Furthermore, the complementary case of a biased intruder in a dense environment of mobile particles on a lattice has also been considered [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Time-dependent dynamics of the three-dimensional driven lattice Lorentz gas

Leitmann

Bénichou

Franosch

2018

J. Phys. A: Math. Theor.

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We consider the motion of a single tracer particle on a three-dimensional lattice in the presence of hard, immobile obstacles at low density. Starting from an equilibrium state, a constant pulling force on the tracer particle is switched on. We elaborate a complete solution for the dynamics, exact in first order of the obstacle density. The time-dependent velocity response and the fluctuations along and perpendicular to the force are derived and compared to stochastic simulations. The non-analytic dependence of the linear-response functions on the frequency, reflecting the long-time tail of the velocity autocorrelation function in equilibrium, has a non-equilibrium analogue in the non-analytic dependence of the stationary velocity as well as the diffusion coefficients as a function of the force. We show that a divergent time scale emerges, separating a regime where linear response is qualitatively correct from a regime where nonlinear effects dominate.

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Section: Calculation Of the Forward-scattering Amplitudementioning

confidence: 99%

Section: Obstacle Obstructed Motionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Time-dependent dynamics of the three-dimensional driven lattice Lorentz gas

Leitmann

Bénichou

Franosch

2018

J. Phys. A: Math. Theor.

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“…[206] was based on a decoupling of the TP-particle-particle correlation function, similar to the one employed in Refs. [125][126][127], and the results were verified numerically and in the high-and low-density of particles limits, in which exact solutions are available [137,[207][208][209]. In particular, it was shown in Ref.…”

Section: 23mentioning

confidence: 60%

Tracer diffusion in crowded narrow channels

Bénichou

Illien

Oshanin

et al. 2018

J. Phys.: Condens. Matter

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We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.

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“…We examine the effects of inner structure of impurity clusters, total drag (friction) force, and possible shock wave enhancement due to collective scattering accompanied by the nonlinear blockade effect in a gas. Note that scattering of driven gas particles was addressed earlier (e.g., [16]) mostly for uniform (on average) distribution of impurities throughout the entire system and in first order of the impurity density (typically ∼ 10 −3 ). Here, we consider the stream scattering on relatively dense ( 10 −1 ) and spatially finite clouds (clusters) of impurities.…”

mentioning

confidence: 99%

Effects of collectively induced scattering of gas stream by impurity ensembles: Shock-wave enhancement and disorder-stimulated nonlinear screening

Kliushnychenko

Lukyanets

2018

Phys. Rev. E

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We report on specific effects of collective scattering for a cloud of heavy impurities exposed to a gas stream. Formation is presented of a common density perturbation and shock waves, both generated collectively by a system of scatterers at sudden application of the stream-inducing external field. Our results demonstrate that (i) the scattering of gas stream can be essentially amplified, due to nonlinear collective effects, upon fragmentation of a solid obstacle into a cluster of impurities (heterogeneously fractured obstacle); (ii) a cluster of disordered impurities can produce considerably stronger scattering accompanied by enhanced and accelerated shock wave, as compared to a regularly ordered cluster. We also show that the final steady-state density distribution is formed as a residual perturbation left after the shock front passage. In particular, a kinklike steady distribution profile can be formed as a result of shock front stopping effect. The possibility of the onset of solitary diffusive density waves, reminiscent of precursor solitons, is shown and briefly discussed.

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Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas

Cited by 5 publications

References 62 publications

Time-dependent dynamics of the three-dimensional driven lattice Lorentz gas

Time-dependent dynamics of the three-dimensional driven lattice Lorentz gas

Tracer diffusion in crowded narrow channels

Effects of collectively induced scattering of gas stream by impurity ensembles: Shock-wave enhancement and disorder-stimulated nonlinear screening

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