Derivation of coupled KPZ-Burgers equation from multi-species zero-range processes

TL;DR

This paper derives a coupled KPZ-Burgers stochastic partial differential equation as the scaling limit of multi-species zero-range processes, extending understanding from single-species to multi-species systems.

Contribution

It introduces the first derivation of a coupled KPZ-Burgers equation from multi-species zero-range processes, revealing new interactions in fluctuation fields.

Findings

Scaling limits of multi-species fluctuation fields solve a coupled Burgers SPDE.

The coupled Burgers SPDE is a spatial gradient of a coupled KPZ equation.

Results extend single-species fluctuation analysis to multi-species systems.

Abstract

We consider the fluctuation fields of multi-species weakly-asymmetric zero-range interacting particle systems in one dimension, where the mass density of each species is conserved. Although such fields have been studied in systems with a single species, the multi-species setting is much less understood. Among other results, we show that, when the system starts from stationary states, with a particular property, the scaling limits of the multi-species fluctuation fields, seen in a characteristic traveling frame, solve a coupled Burgers SPDE, which is a formal spatial gradient of a coupled KPZ equation.