Coupled Kardar-Parisi-Zhang Equations in One Dimension

TL;DR

This paper extends the understanding of one-dimensional KPZ equations to coupled systems, establishing theoretical equivalences and validating predictions through detailed Monte Carlo simulations of a specific lattice gas model.

Contribution

It introduces a framework for coupled KPZ equations, links them to nonlinear fluctuating hydrodynamics, and confirms theoretical predictions with microscopic simulations.

Findings

Confirmed scaling exponents and functions in coupled KPZ systems

Derived coefficients from microscopic lattice models

Validated theoretical predictions with Monte Carlo simulations

Abstract

Over the past years our understanding of the scaling properties of the solutions to the one-dimensional KPZ equation has advanced considerably, both theoretically and experimentally. In our contribution we export these insights to the case of coupled KPZ equations in one dimension. We establish equivalence with nonlinear fluctuating hydrodynamics for multi-component driven stochastic lattice gases. To check the predictions of the theory, we perform Monte Carlo simulations of the two-component AHR model. Its steady state is computed using the matrix product ansatz. Thereby all coefficients appearing in the coupled KPZ equations are deduced from the microscopic model. Time correlations in the steady state are simulated and we confirm not only the scaling exponent, but also the scaling function and the non-universal coefficients.