Evidence for Geometry-Dependent Universal Fluctuations of the Kardar-Parisi-Zhang Interfaces in Liquid-Crystal Turbulence
By K. Takeuchi, Masaki Sano. 2012
165 citations recorded by the source corpus.
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 [Takeuchi and Sano in Phys. Rev. Lett. 104:230601, 2010; Takeuchi et al. in 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.
Subfields: Condensed Matter Physics, Economics and Econometrics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/0e224c40899ae20e72b303e45f6c225f37ab2174
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Citations in the corpus
- Operator Spreading in Random Unitary Circuits (2017, methodology): “For the growth of a droplet, the probability distribution of the interface radius is given by the GUE Tracy Widom distribution [65, 68] (which has been been observed experimentally in striking experiments on the growth of a turbulent domain in liquid crystals [93, 94]).”
- An appetizer to modern developments on the Kardar–Parisi–Zhang universality class (2017, methodology): “Indeed, there is now overwhelming evidence that this geometry dependence is not a special property of the PNG model; instead, it is known to occur in various models [14–18] and in experiments [20, 21] as well.”
- Extreme value statistics of correlated random variables: A pedagogical review (2019, unknown): “[211] K .”
- Quantum Entanglement Growth Under Random Unitary Dynamics (2016, background): “It captures an important universality class which has found a wealth of applications in classical nonequilibrium physics, and its scaling properties have been verified in high-precision experiments [38, 39].”
- The One-Dimensional KPZ Equation and Its Universality Class (2015, background): “The most prominent physical realization is a thin film of turbulent liquid crystal [9,10].”
- Free Energy Fluctuations for Directed Polymers in Random Media in 1 + 1 Dimension (2012, background): “The scalings and do not change, but the limiting statistics reflect the initial data (see the reviews [29, 30] and recent experiments [61]).”
- The nonperturbative functional renormalization group and its applications (2020, background): “dimensions, sustained by a wealth of exact results [417], and by high-precision measurements in turbulent convection of liquid crystals [418, 419].”