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      Logarithmic superdiffusion in two dimensional driven lattice gases

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          Abstract

          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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          Large-distance and long-time properties of a randomly stirred fluid

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            A pedestrian's view on interacting particle systems, KPZ universality, and random matrices

            These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy-Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.
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              Field theory of long time behaviour in driven diffusive systems

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                Author and article information

                Journal
                10 November 2017
                Article
                1711.03728
                79607f2f-9354-42e0-a78a-f23fce80997a

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                14 pages, 4 figures
                cond-mat.stat-mech

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