The Popkov-Schütz two-lane lattice gas: Universality for general jump rates

TL;DR

The paper investigates a two-lane, exclusion-type lattice gas (Popkov-Schütz model) with general jump rates under a product-form stationary measure, focusing on the degenerate flux Jacobian that occurs at half-filling ($\rho_1=\rho_2=\tfrac{1}{2}$). By computing the second-order expansion of the steady-state currents around this point, the linear term vanishes and the quadratic form becomes controlled solely by the stationary parameter $q = e^{\nu}-1$, up to an overall time scale. After a $\pi/4$ rotation, the quadratic current determines the associated universality class, which is then connected to continuum coupled Burgers equations with coupling parameter $X = \frac{\sqrt{1+q}}{2\sqrt{1+q}-1}$; the diagonal $X=Y$ case yields a four-parameter universality class, with TASEP corresponding to a single point. The results clarify how degenerate multi-component driven lattice gases organize into distinct universality classes and provide a framework for exploring the impact of model parameters on macroscopic fluctuations and scaling behavior.

Abstract

We consider the asymmetric version of the Popkov-Schütz two-lane lattice gas with general jump rates, subject to the stationary measure being of product form. This still leaves five free parameters. At density 1/2 the eigenvalues of the flux Jacobian are degenerate. We compute the second order expansion of the average fluxes at density 1/2 and thereby identify the universality classes.