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

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 two locally conserved fields. The peak structure of their steady state space–time correlations is determined through numerical simulations 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 maximally asymmetric Lévy distribution with parameter α=5/3. As a by-product, we completely classify the universality classes for two coupled stochastic Burgers equations with arbitrary coupling coefficients.