Dynamics of growing surfaces by linear equations in2+1dimensions

Abstract

An extensive study on the (2+1) -dimensional super-rough growth processes, described by a special class of linear growth equations, is undertaken. This special class of growth equations is of theoretical interests since they are exactly solvable and thus provide a window for understanding the intriguing anomalous scaling behaviors of super-rough interfaces. We first work out the exact solutions of the interfacial heights and the equal-time height difference correlation functions. Through our rigorous analysis, the detailed asymptotics of the correlation function in various time regimes are derived. Our obtained analytical results not only affirm the applicability of anomalous dynamic scaling ansatz but also offer a solid example for understanding a distinct universal feature of super-rough interfaces: the local roughness exponent is always equal to 1. Furthermore, we also perform some numerical simulations for illustration. Finally, we discuss what are the essential ingredients for constructing super-rough growth equations.