Research Abstract


Growing interfaces uncover universal fluctuations behind scale invariance

2011年7月11日 Scientific Reports 1 : 34 doi: 10.1038/srep00034


竹内一将1,佐野雅己1,笹本智弘2 & Herbert Spohn3

  1. 東京大学 理学系研究科
  2. 千葉大学 理学研究科
  3. ミュンヘン工科大学(独)
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.