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arXiv · 1108.2118

Growing interfaces uncover universal fluctuations behind scale invariance

Kazumasa A. Takeuchi·Masaki Sano·Tomohiro Sasamoto·Herbert Spohn
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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.

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Kazumasa A. Takeuchi, Masaki Sano, Tomohiro Sasamoto, Herbert Spohn. 2011-08-10. Growing interfaces uncover universal fluctuations behind scale invariance. https://doi.org/10.1038/srep00034

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