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

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.