A lattice gas model for generic one-dimensional Hamiltonian Systems

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

References in corpus (4)

• Exact scaling functions for one-dimensional stationary KPZ growth
• Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields
• Exact scaling solution of the mode coupling equations for non-linear fluctuating hydrodynamics in one dimension
• Dynamics of coupled modes for sliding particles on a fluctuating landscape