Nonlinear Fluctuating Hydrodynamics in One Dimension: the Case of Two Conserved Fields

TL;DR

This paper investigates the BS model, a one-dimensional lattice field theory with two conserved fields, analyzing its steady state correlations and confirming predictions from nonlinear fluctuating hydrodynamics, including KPZ and Levy scaling behaviors.

Contribution

It provides the first detailed numerical validation of nonlinear fluctuating hydrodynamics predictions for a two-field model and classifies universality classes for coupled stochastic Burgers equations.

Findings

Confirmation of KPZ scaling for traveling peaks.

Observation of Levy distribution scaling for standing peaks.

Complete classification of universality classes for two coupled Burgers equations.

Abstract

We study the BS model, which is a one-dimensional lattice field theory taking real values. Its dynamics is governed by coupled differential equations plus random nearest neighbor exchanges. The BS model has exactly two locally conserved fields. Through numerical simulations the peak structure of the steady state space-time correlations is determined and compared with nonlinear fluctuating hydrodynamics, which predicts a traveling peak with KPZ scaling function and a standing peak with a scaling function given by the completely asymmetric Levy distribution with parameter $\alpha = 5/3$. As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.