https://doi.org/10.1140/epjb/e2003-00066-x
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 ealbano@inifta.unlp.edu.ar
Received:
26
August
2002
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
