Growing interfaces uncover universal fluctuations behind scale invariance

TL;DR

This paper demonstrates universal fluctuations in growing interfaces, linking experimental liquid-crystal turbulence data with exact solutions of the KPZ equation, revealing universal distributions akin to random matrix theory.

Contribution

It provides the first experimental verification of universal distributions in interface growth and offers an exact solution to the KPZ equation for different geometries.

Findings

Universal scaling laws observed in liquid-crystal turbulence

Interface position distributions match random matrix theory predictions

Distinct distributions for curved and flat interfaces

Abstract

Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a line, though it is also scale-invariant and arises in nature as various types of interface growth, is far less understood. The two major missing ingredients are: an experiment that allows a quantitative comparison with theory and an analytic solution of the Kardar-Parisi-Zhang (KPZ) equation, a prototypical equation for describing growing interfaces. Here we solve both problems, showing unprecedented universality beyond the scaling laws. We investigate growing interfaces of liquid-crystal turbulence and find not only universal scaling, but universal distributions of interface positions. They obey the largest-eigenvalue distributions of random matrices and depend on whether the interface is curved or flat, albeit universal in each case. Our exact solution of the KPZ equation provides theoretical explanations.