Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence

TL;DR

This paper demonstrates that liquid-crystal turbulence interfaces exhibit universal fluctuations consistent with the KPZ class, with statistical properties depending on the global geometry of the interfaces, such as circular or flat shapes.

Contribution

It provides detailed experimental evidence that KPZ universality applies to liquid-crystal turbulence interfaces, including distribution functions and correlation functions, highlighting geometry-dependent universal behavior.

Findings

Fluctuations follow KPZ scaling exponents.

Distribution and correlation functions match solvable KPZ models.

Universal properties depend on interface geometry.

Abstract

We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1 dimensions [Phys. Rev. Lett. 104, 230601 (2010); Sci. Rep. 1, 34 (2011)]. Here we investigate both circular and flat interfaces and report their statistics in detail. First we demonstrate that their fluctuations show not only the KPZ scaling exponents but beyond: they asymptotically share even the precise forms of the distribution function and the spatial correlation function in common with solvable models of the KPZ class, demonstrating also an intimate relation to random matrix theory. We then determine other statistical properties for which no exact theoretical predictions were made, in particular the temporal correlation function and the persistence probabilities. Experimental results on finite-time effects and extreme-value statistics are also presented. Throughout the paper, emphasis is put on how the universal statistical properties depend on the global geometry of the interfaces, i.e., whether the interfaces are circular or flat. We thereby corroborate the powerful yet geometry-dependent universality of the KPZ class, which governs growing interfaces driven out of equilibrium.