1208.5147 (David Hansmann et al.)

Coarse grained approach for volume conserving models    [PDF]

David Hansmann, Rubén C. Buceta

Volume conserving surface models (VCS) without deposition and evaporation, as flux free ideal molecular-beam epitaxy models, are prototypes to study of the symmetries of conserved dynamics. In this work we study two similar VCS models with conserved noise, which differ from each other by the axial symmetry of their dynamic hopping rules. We use a coarse-grained approach to analyze the models and show how to determine the coefficients of their related continuous stochastic differential equation (SDE). The employed method makes use of small translations in a test space, where the test space, which considers the implicit symmetries of the system, contains the stationary probability density function (spdf). In case of the symmetric model we calculate all the coarse-grained coefficients of the related conserved Kardar-Parisi-Zhang (KPZ) equation. Further we determine the implicit relation between the coefficients and the intensity of conserved noise. With respect to the symmetric model, the asymmetric model adds new terms which have to be analyzed, first of all the diffusion term, whose coarse-grained coefficient can be determined by the same method. In contrast to other methods, the used formalism allows to calculate all coefficients of the SDE theoretically and within limits numerically. Above all, the used approach connects the coefficients of the SDE with the spdf and hence gives them a precise physical meaning.

View original: http://arxiv.org/abs/1208.5147