A lattice Gas Model for Generic One-Dimensional Hamiltonian Systems

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 Prahofer-Spohn scaling function) and a superdiffusive heat mode with dynamical exponent z = 5/3 and symmetric Levy 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-Levy-mode gives at least the right order of magnitude. (iii) There are significant diffusive corrections which are non-universal.