Edwards-Wilkinson surface over a spherical substrate: $1/f$ noise in the height fluctuations

TL;DR

This paper analyzes the steady state height fluctuations of an Edwards-Wilkinson surface on a spherical substrate, revealing that fluctuations exhibit Gaussian 1/f noise characteristics similar to those on planar surfaces, with a latitude-independent effective surface tension.

Contribution

It demonstrates that the 1/f noise behavior of height fluctuations persists on a spherical substrate and that the effective surface tension remains constant across latitudes.

Findings

Height fluctuations follow Gaussian 1/f noise on a sphere.

Effective surface tension is independent of latitude.

Fluctuation behavior matches that of planar substrates.

Abstract

We study the steady state fluctuations of an Edwards-Wilkinson type surface with the substrate taken to be a sphere. We show that the height fluctuations on circles at a given latitude has the effective action of a perfect Gaussian $1/f$ noise, just as in the case of fixed radius circles on an infinite planar substrate. The effective surface tension, which is the overall coefficient of the action, does not depend on the latitude angle of the circles.