Diffusivity of Lattice Gases

Quastel, Jeremy; Valkó, Benedek

doi:10.1007/s00205-013-0651-7

Cited by 7 publications

(5 citation statements)

References 39 publications

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“…One might ask whether, similarly to the intermediate disorder case, it is then possible to consider the model on larger scales and still obtain convergence to KPZ (or some other non-Gaussian process). By analogy with what happens in the context of lattice gases, we do not expect this to be the case [QV13].…”

mentioning

confidence: 92%

A Class of Growth Models Rescaling To kpz

Hairer

Quastel

2018

Forum of Mathematics, Pi

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176

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mentioning

confidence: 92%

A Class of Growth Models Rescaling To kpz

Hairer

Quastel

2018

Forum of Mathematics, Pi

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176

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“…( 5) for t = 100. the standard RW result, which may be either a very small power-law s(t) ∼ t 0.06... or a logarithmic correction s(t) ∼ (ln t) γ , and it is difficult to distinguish between the two behaviors based on our numerics [21] -as is often the case with marginal corrections [29][30][31][32]. Such logarithmic corrections have been found earlier in twodimensional driven diffusive systems [22,[33][34][35] as well as for 1 + 1 dimensional interface with cubic nonlinearity [36][37][38][39].…”

mentioning

confidence: 84%

Statistics of overtake events by a tagged agent

Das¹,

Dhar²,

Sabhapandit³

2018

Phys. Rev. E

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We consider a one-dimensional infinite lattice where at each site there sits an agent carrying a velocity, which is drawn initially for each agent independently from a common distribution. This system evolves as a Markov process where a pair of agents at adjacent sites exchange their positions with a specified rate, while retaining their respective velocities, only if the velocity of the agent on the left site is higher. We study the statistics of the net displacement of a tagged agent m(t) on the lattice, in a given duration t, for two different kinds of rates: one in which a pair of agents at sites i and i + 1 exchange their sites with rate 1, independent of the velocity difference between the neighbors, and another in which a pair exchange their sites with a rate equal to their relative speed. In both cases, we find m(t) ∼ t for large t. In the first case, for a randomly picked agent, m/t, in the limit t → ∞, is distributed uniformly on [−1, 1] for all continuous distributions of velocities. In the second case, the distribution is given by the distribution of the velocities itself, with a Galilean shift by the mean velocity. We also find the large time approach to the limiting forms and compare the results with numerical simulations. In contrast, if the exchange of velocities occurs at unit rate, independent of their values, and irrespective of which is faster, m(t)/t for large t is has a gaussian distribution, whose width varies as t −1/2 .

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“…Applying this approximation to the system of interest with anisotropy parameter p, we have the current-density relation 17) and the diffusion matrix D p = diag (D T,p , D S,p ). Under the reasonable assumption that the diffusion constants scale linearly with the probability of motion in the respective direction, we expect…”

Section: Mode Coupling Theorymentioning

confidence: 99%

“…On physical grounds one expects the same behavior to apply throughout the class of two-dimensional DDS, but extending the result of Yau to a more general setting has so far remained elusive. In recent work the existence of logarithmic superdiffusivity has been established for a fairly broad class of models, but only upper and lower bounds 1/2 ≤ ζ ≤ 1 were obtained for the exponent of the logarithmic correction [17].…”

Section: Introductionmentioning

confidence: 99%

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

Krug¹,

Neiss²,

Schadschneider³

et al. 2018

J Stat Phys

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The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t) 2/3 with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.

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Diffusivity of Lattice Gases

Cited by 7 publications

References 39 publications

A Class of Growth Models Rescaling To kpz

A Class of Growth Models Rescaling To kpz

Statistics of overtake events by a tagged agent

Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases

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