Crossover of interfacial dynamics

Some dynamical models in which there is a significant interplay between interfacial and bulk degrees of freedom are treated at the mean-field (or Van Hove) level from a coarse-grained microscopic viewpoint. Specifically, the near-equilibrium interfacial dynamics of two of the simplest models with conservation laws, models B and C, are studied with use of (as appropriate) variational techniques, perturbation theory, and (with certain additional simplifications) exact solutions. Use of these methods allows the dispersion relation for interfacial modes to be interpolated between the ‘‘hydrodynamical’’ and critical regimes. The crossover scaling behavior lends support to renormalization-group methods near d=1 which focus on the interfacial modes but nonetheless extract the bulk dynamical exponent as well as the crossover.