Drift causes anomalous exponents in growth processes

TL;DR

This paper investigates how drift terms influence growth exponents in one-dimensional growth processes, revealing a mechanism that alters expected scaling behavior and impacts interpretation of experimental and numerical results.

Contribution

It identifies a general mechanism where drift causes a change in exponents, challenging traditional dimensional analysis predictions in growth models.

Findings

Drift induces a change in the roughness and growth exponents.

The mechanism causes exponents to coincide, deviating from standard predictions.

This effect is relevant for interpreting experimental and numerical data.

Abstract

The effect of a drift term in the presence of fixed boundaries is studied for the one-dimensional Edwards-Wilkinson equation, to reveal a general mechanism that causes a change of exponents for a very broad class of growth processes. This mechanism represents a relevant perturbation and therefore is important for the interpretation of experimental and numerical results. In effect, the mechanism leads to the roughness exponent assuming the same value as the growth exponent. In the case of the Edwards-Wilkinson equation this implies exponents deviating from those expected by dimensional analysis.