Universality classes in two-component driven diffusive systems

TL;DR

This paper identifies new universality classes in driven diffusive systems with two conserved densities, revealing distinct dynamical exponents and scaling behaviors not previously reported, through extensive Monte Carlo simulations and theoretical analysis.

Contribution

It provides the first numerical evidence for novel universality classes with specific dynamical exponents in two-component driven diffusive systems, supported by mode coupling theory.

Findings

Discovery of universality classes with exponents z=(1+√5)/2 and z=3/2.

Numerical convergence towards asymmetric Lévy scaling functions for superdiffusive modes.

Universality classes are determined by the current-density relation and compressibility matrix.

Abstract

We study time-dependent density fluctuations in the stationary state of driven diffusive systems with two conserved densities $\rho_\lambda$. Using Monte-Carlo simulations of two coupled single-lane asymmetric simple exclusion processes we present numerical evidence for universality classes with dynamical exponents $z=(1+\sqrt{5})/2$ and $z=3/2$ (but different from the Kardar-Parisi-Zhang (KPZ) universality class), which have not been reported yet for driven diffusive systems. The numerical asymmetry of the dynamical structure functions converges slowly for some of the non-KPZ superdiffusive modes for which mode coupling theory predicts maximally asymmetric $z$-stable L\'evy scaling functions. We show that all universality classes predicted by mode coupling theory for two conservation laws are generic: They occur in two-component systems with nonlinearities in the associated currents already of the minimal order $\rho_\lambda^2\rho_\mu$. The macroscopic stationary current-density relation and the compressibility matrix determine completely all permissible universality classes through the mode coupling coefficients which we compute explicitly for general two-component systems.