English

A lattice gas model for generic one-dimensional Hamiltonian Systems

Statistical Mechanics 2021-04-21 v1

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=3/2z=3/2 and symmetric Pr\"ahofer-Spohn scaling function) and a superdiffusive heat mode with dynamical exponent z=5/3z=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 5/35/3-L\'evy-mode gives at least the right order of magnitude. (iii) There are significant diffusive corrections which are non-universal.

Keywords

Cite

@article{arxiv.2011.02940,
  title  = {A lattice gas model for generic one-dimensional Hamiltonian Systems},
  author = {Johannes Schmidt and Gunter M. Schütz and Henk van Beijeren},
  journal= {arXiv preprint arXiv:2011.02940},
  year   = {2021}
}
R2 v1 2026-06-23T19:56:35.227Z