Bulk dynamics for interfacial growth models

We study the influence of the bulk dynamics of a growing cluster of particl es on the properties of its interface. First, we define a general bulk grow th model by means of a continuum Master equation for the evolution of the b ulk density field. This general model just considers an arbitrary addition of particles (though it can be easily generalized to consider subtraction) with no other physical restriction. The corresponding Langevin equation for this bulk density field is derived where the influence of the bulk dynamic s is explicitly shown. Finally, when a well-defined interface is assumed fo r the growing cluster, the Langevin equation for the height field of this i nterface for some particular bulk dynamics is written. In particular, we ob tain the celebrated Kardar-Parisi-Zhang equation. A Monte Carlo simulation illustrates the theoretical results.