Scaling and universality in coupled driven diffusive models

Abstract

Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled Burgers-likemodel in one dimension (1d), a generalization of the Burgers model to coupleddegrees of freedom, is proposed to describe 1dMHD. In addition to MHD, thismodel serves as a 1d reduced model for driven binary fluid mixtures. Here we haveperformed a comprehensive study of the universal properties of the generalizedd-dimensional version of the reduced model. We employ both analytical and numericalapproaches. In particular, we determine the scaling exponents and the amplitude ratios ofthe relevant two-point time-dependent correlation functions in the model. We demonstratethat these quantities vary continuously with the amplitude of the noise cross-correlation.Further our numerical studies corroborate the continuous dependence of long wavelengthand long timescale physics of the model on the amplitude of the noise cross-correlations, asfound in our analytical studies. We construct and simulate lattice–gas models of coupleddegrees of freedom in 1d, belonging to the universality class of our coupled Burgers-likemodel, which display similar behavior. We use a variety of numerical (MonteCarlo and Pseudo-spectral methods) and analytical (dynamic renormalizationgroup, self-consistent mode coupling theory and functional renormalization group)approaches for our work. The results from our different approaches complement oneanother. Possible realizations of our results in various non-equilibrium models arediscussed.