Kinetic roughening, global quantities, and fluctuation-dissipation relations

TL;DR

This paper introduces a new global quantity for studying interface roughness that better captures interface properties and obeys fluctuation-dissipation relations, enabling more consistent analysis of growth processes.

Contribution

It proposes a novel global quantity linked to interface roughness that is experimentally accessible and satisfies fluctuation-dissipation relations in equilibrium.

Findings

The new global quantity provides a better measure of interface roughness.

It obeys the fluctuation-dissipation theorem in steady state.

Analytic results are derived for Edwards-Wilkinson and Mullins-Herring models.

Abstract

Growth processes and interface fluctuations can be studied through the properties of global quantities. We here discuss a global quantity that not only captures better the roughness of an interface than the widely studied surface width, but that is also directly conjugate to an experimentally accessible parameter, thereby allowing us to study in a consistent way the global response of the system to a global change of external conditions. Exploiting the full analyticity of the linear Edwards-Wilkinson and Mullins-Herring equations, we study in detail various two-time functions related to that quantity. This quantity fulfills the fluctuation-dissipation theorem when considering steady-state equilibrium fluctuations.