Universality in coupled stochastic Burgers systems with degenerate flux Jacobian

TL;DR

This paper investigates coupled stochastic Burgers systems with degenerate flux Jacobian, demonstrating universality in their behavior and confirming a dynamical exponent of 3/2 through analysis of correlations and currents.

Contribution

It introduces a coupled stochastic Burgers model with degenerate flux Jacobian and shows its universality class matches that of a two-lane lattice gas, extending understanding of such systems.

Findings

Confirmed dynamical exponent 3/2 for specific couplings

Demonstrated universality between continuum and lattice models

Analyzed spacetime correlations of conserved fields

Abstract

In our contribution we study stochastic models in one space dimension with two conservation laws. One model is the coupled continuum stochastic Burgers equation, for which each current is a sum of quadratic non-linearities, linear diffusion, and spacetime white noise. The second model is a two-lane stochastic lattice gas. As distinct from previous studies, the two conserved densities are tuned such that the flux Jacobian, a $2 \times 2$ matrix, has coinciding eigenvalues. In the steady state, investigated are spacetime correlations of the conserved fields and the time-integrated currents at the origin. For a particular choice of couplings the dynamical exponent 3/2 is confirmed. Furthermore, at these couplings, continuum stochastic Burgers equation and lattice gas are demonstrated to be in the same universality class.