Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

HOROWITZ CLAUDIO; ALBANO EZEQUIEL

EUROPEAN PHYSICAL JOURNAL B - CONDENSED MATTER

EDP Science

Año: 2003 vol. 31 p. 563 - 568

1434-6028

The relationship between a microscopic parameter “p”, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface´s evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both  and  depend on p in the following way: (p)=p and (p)=p3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where  depends on p according to (p)=p2 . It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models.