Details

Autor(en) / Beteiligte

• Takeuchi, Kazumasa A
• Sano, Masaki
• Sasamoto, Tomohiro
• Spohn, Herbert

Titel

Growing interfaces uncover universal fluctuations behind scale invariance

Ist Teil von

• Scientific reports, 2011-07, Vol.1 (1), p.34-34, Article 34

Ort / Verlag

England: Nature Publishing Group

Erscheinungsjahr

2011

Link zum Volltext

Quelle

Electronic Journals Library

Beschreibungen/Notizen

• 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.