Correlation functions and queuing phenomena in growth processes with drift
Abstract
We suggest a novel stochastic discrete growth model which describes the drifted Edward-Wilkinson (EW) equation
∂h/∂t=ν
∂
2
x
h−v
∂
x
h+η(x,t)
. From the stochastic model, the anomalous behavior of the drifted EW equation with a defect is analyzed. To physically understand the anomalous behavior the height-height correlation functions
C(r)=<|h(
x
0
+r)−h(
x
0
)|>
and
G(r)=<|h(
x
0
+r)−h(
x
0
)
|
2
>
are also investigated, where the defect is located at
x
0
. The height-height correlation functions follow the power law
C(r)∼
r
α
′
and
G(r)∼
r
α
′′
with
α
′
=
α
′′
=1/4
around a perfect defect at which no growth process is allowed.
α
′
=
α
′′
=1/4
is the same as the anomalous roughness exponent
α=1/4
. For the weak defect at which the growth process is partially allowed, the normal EW behavior is recovered. We also suggest a new type queuing process based on the asymmetry
C(r)≠C(−r)
of the correlation function around the perfect defect.