Weak and strong dynamic scaling in a one-dimensional driven coupled-field model: Effects of kinematic waves - art. no. 021402

We study the coupled dynamics of the displacement fields in a one-dimension al coupled-field model for drifting crystals, first proposed by Lahiri and Ramaswamy [Phys. Rev. Lett. 79, 1150 (1997)]. We present some exact results for the steady state and the current in the lattice version of the model f or a special subspace in the parameter space, within the region where the m odel displays kinematic waves. We use these results to construct the effect ive continuum equations corresponding to the lattice model. These equations decouple at the linear level in terms of the eigenmodes. We examine the lo ng-time, large-distance properties of the correlation functions of the eige nmodes by using symmetry arguments, Monte Carlo simulations, and self-consi stent mode-coupling methods. For most parameter values, the scaling exponen ts of the Kardar-Parisi-Zhang equation are obtained. However, for certain s ymmetry-determined values of the coupling constants the two eigenmodes, alt hough nonlinearly coupled, are characterized by two distinct dynamic expone nts. We discuss the possible application of the dynamic renormalization gro up in this context.