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arXiv · 2011.02940

A lattice gas model for generic one-dimensional Hamiltonian Systems

Johannes Schmidt·Gunter M. Schütz·Henk van Beijeren
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Abstract

We present a three-lane exclusion process that exhibits the same universal fluctuation pattern as generic one-dimensional Hamiltonian dynamics with short-range interactions, viz., with two sound modes in the Kardar-Parisi-Zhang (KPZ) universality class (with dynamical exponent $z=3/2$ and symmetric Pr\"ahofer-Spohn scaling function) and a superdiffusive heat mode with dynamical exponent $z=5/3$ and symmetric L\'evy scaling function. The lattice gas model is amenable to efficient numerical simulation. Our main findings, obtained from dynamical Monte-Carlo simulation, are: (i) The frequently observed numerical asymmetry of the sound modes is a finite time effect. (ii) The mode-coupling calculation of the scale factor for the $5/3$-L\'evy-mode gives at least the right order of magnitude. (iii) There are significant diffusive corrections which are non-universal.

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Johannes Schmidt, Gunter M. Schütz, Henk van Beijeren. 2020-11-05. A lattice gas model for generic one-dimensional Hamiltonian Systems. https://doi.org/10.1007/s10955-021-02709-1

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