Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals

2010/01/31 by Kazumasa A. Takeuchi, Masaki Sano · 363 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Liquid crystal #Materials science #Mechanics #Physics #Random Matrices and Applications #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Turbulence #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1103/physrevlett.104.230601

published in Physical Review Letters 104(23), 230601 (American Physical Society) · 4 pages, 5 figures; minor changes made; note added

openalex publication_date 2010/06/11 · arxiv created 2010/06/14 · arxiv updated 2010/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• The Physics of Liquid Crystals
• Dynamic Scaling of Non-Euclidean Interfaces
• The Airy1 Process is not the Limit of the Largest Eigenvalue in GOE Matrix Diffusion
• Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals
• Fredholm determinants, differential equations and matrix models

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