# Symmetries and scaling in generalised coupled conserved Kardar-Parisi-Zhang equations

## TL;DR

This paper investigates the universal scaling behaviors of a conserved density coupled to a fluctuating surface described by the conserved KPZ equation, revealing how symmetries influence nonequilibrium universality classes.

## Contribution

It introduces two minimal models of conserved density coupled to surface fluctuations, analyzing their universal scaling properties and the role of symmetries in nonequilibrium universality classes.

## Key findings

- Identified universal scaling properties of conserved densities in coupled KPZ systems.
- Demonstrated how different symmetry considerations lead to distinct universality classes.
- Highlighted the influence of conservation laws and symmetries on nonequilibrium critical behavior.

## Abstract

We study the noisy nonequilibrium dynamics of a conserved density that is driven by a fluctuating surface governed by the conserved Kardar-Parisi-Zhang equation. We uncover the universal scaling properties of the conserved density. We consider two separate minimal models where the surface fluctuations couple (i) with the spatial variation of the conserved density, and (ii) directly with the magnitude of the conserved density. Both these two models conserve the density, but differ from symmetry stand point. We use our result to highlight the dependence of nonequilibrium universality classes on the interplay between symmetries and conservation laws.