A lattice gas model for generic one-dimensional Hamiltonian Systems

TL;DR

This paper introduces a three-lane exclusion process model that replicates the universal fluctuation patterns of one-dimensional Hamiltonian systems, including sound and heat modes, verified through numerical simulations.

Contribution

The paper presents a new lattice gas model that captures the universal fluctuation behavior of 1D Hamiltonian systems, facilitating efficient numerical analysis.

Findings

Finite time effects cause observed asymmetry in sound modes.

Mode-coupling calculations approximate the scale factor for the Lévý heat mode.

Significant non-universal diffusive corrections are present.

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.