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arXiv · 1711.03728

Logarithmic superdiffusion in two dimensional driven lattice gases

Joachim Krug·Robert A. Neiss·Andreas Schadschneider·Johannes Schmidt
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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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Joachim Krug, Robert A. Neiss, Andreas Schadschneider, Johannes Schmidt. 2017-11-10. Logarithmic superdiffusion in two dimensional driven lattice gases. https://doi.org/10.1007/s10955-018-1995-z

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