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 $\partial h/\partial t=\nu {\partial }_x^{2}h-v{\partial }_{x}h+\eta (x,t)$. 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 $C(r)\sim r^{{\alpha }^{\prime }}$ and $G(r)\sim r^{{\alpha }^{\prime \prime }}$ with ${\alpha }^{\prime }={\alpha }^{\prime \prime }=1/4$ around a perfect defect at which no growth process is allowed. ${\alpha }^{\prime }={\alpha }^{\prime \prime }=1/4$ is the same as the anomalous roughness exponent $\alpha =1/4$. 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 $C(r)\ne C(-r)$ of the correlation function around the perfect defect.