Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models
Instituto de Investigaciones Fisicoquímicas Teóricas
y Aplicadas, (INIFTA), CONICET, UNLP.
Sucursal 4, Casilla de Correo 16, (1900) La Plata, Argentina
Corresponding author: a email@example.com
Revised: 20 November 2002
Published online: 6 March 2003
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 λ and ν depend on p in the following way: and . 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 ν depends on p according to . 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.
PACS: 68.35.Ct – Interface structure and roughness / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics / 81.15.Aa – Theory and models of film growth
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003