Interface motion in models with stochastic dynamics

We derive the phenomenological dynamics of interfaces from stochastic microscopic models. The main emphasis is on models with a nonconserved order parameter. A slowly varying interface has then a local normal velocity proportional to the local mean curvature. We study bulk models and effective interface models and obtain Green-Kubo-like expressions for the mobility. Also discussed are interface motion in the case of a conserved order parameter, pure surface diffusion, and interface fluctuations. For the two-dimensional Ising model at zero temperature, motion by mean curvature is established rigorously.     

Thermal Conductivity for a Noisy Disordered Harmonic Chain

We consider a d-dimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the Green-Kubo formula. These bounds indicate a positive finite conductivity. We prove also that the infinite volume homogenized Green-Kubo formula converges.     

Staggered diffusivities in lattice gas cellular automata

The majority of LGCAs has spurious conservation laws, the so-called staggered invariants, first discovered by Kadanoff, McNamara, and Zanetti. Consequently there are additional hydrodynamic modes of diffusive type, which modify mode coupling theories and the nonlinear fluid dynamic equations. The diffusivities of these staggered modes are evaluated in the mean field approximation for LGCAs on triangular lattices, starting from the Green-Kubo formulas for the staggered diffusivities.