Universality classes in two-component driven diffusive systems

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 $z=(1+\sqrt{5})\mathrm{/}2$ and $z=3\mathrm{/}2$ (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.