Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals

TL;DR

This paper provides experimental evidence that the fluctuations of growing interfaces in turbulent liquid crystals follow universal statistical laws described by the KPZ theory and random matrix theory, revealing scale-invariant behavior.

Contribution

It demonstrates that interface fluctuations in turbulent liquid crystals exhibit universal scaling and distribution properties predicted by KPZ and random matrix theories.

Findings

Interface roughening follows KPZ scaling laws.

Fluctuation distributions are governed by the largest eigenvalue of random matrices.

Provides experimental evidence of universality in turbulent liquid crystal interfaces.

Abstract

We investigate growing interfaces of topological-defect turbulence in the electroconvection of nematic liquid crystals. The interfaces exhibit self-affine roughening characterized by both spatial and temporal scaling laws of the Kardar-Parisi-Zhang theory in 1+1 dimensions. Moreover, we reveal that the distribution and the two-point correlation of the interface fluctuations are universal ones governed by the largest eigenvalue of random matrices. This provides quantitative experimental evidence of the universality prescribing detailed information of scale-invariant fluctuations.