Correlation functions and queuing phenomena in growth processes with drift

TL;DR

This paper introduces a stochastic growth model for the drifted Edwards-Wilkinson equation, analyzes correlation functions near defects, and reveals anomalous roughness behavior and a new queuing process related to defect asymmetry.

Contribution

It presents a novel stochastic model for the drifted EW equation with defects, analyzing correlation functions and discovering anomalous roughness and a new queuing process.

Findings

Correlation functions follow power laws with exponent 1/4 near perfect defects.

Anomalous roughness exponent is identified as 1/4.

A new queuing process is proposed based on correlation asymmetry.

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 $C(r)\sim r^{\alpha'}$ and $G(r)\sim r^{\alpha''}$ with $\alpha'=\alpha''=1/4$ around a perfect defect at which no growth process is allowed. $\alpha'=\alpha''=1/4$ 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 $C(r) \neq C(-r)$ of the correlation function around the perfect defect.