Fukai Yohsuke T, Takeuchi Kazumasa A
Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan.
Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8551, Japan.
Phys Rev Lett. 2017 Jul 21;119(3):030602. doi: 10.1103/PhysRevLett.119.030602.
We study the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces growing inward from ring-shaped initial conditions, experimentally and numerically, using growth of a turbulent state in liquid-crystal electroconvection and an off-lattice Eden model, respectively. To realize the ring initial condition experimentally, we introduce a holography-based technique that allows us to design the initial condition arbitrarily. Then, we find that fluctuation properties of ingrowing circular interfaces are distinct from those for the curved or circular KPZ subclass and, instead, are characterized by the flat subclass. More precisely, we find an asymptotic approach to the Tracy-Widom distribution for the Gaussian orthogonal ensemble and the Airy_{1} spatial correlation, as long as time is much shorter than the characteristic time determined by the initial curvature. Near this characteristic time, deviation from the flat KPZ subclass is found, which can be explained in terms of the correlation length and the circumference. Our results indicate that the sign of the initial curvature has a crucial role in determining the universal distribution and correlation functions of the KPZ class.
我们分别通过液晶电对流中的湍流状态增长以及非晶格伊登模型，对从环形初始条件向内生长的（1 + 1）维 Kardar-Parisi-Zhang（KPZ）界面进行了实验和数值研究。为了通过实验实现环形初始条件，我们引入了一种基于全息术的技术，该技术使我们能够任意设计初始条件。然后，我们发现向内生长的圆形界面的涨落特性与弯曲或圆形 KPZ 子类的不同，相反，其特征在于平坦子类。更确切地说，只要时间远短于由初始曲率确定的特征时间，我们发现高斯正交系综的 Tracy-Widom 分布和 Airy₁ 空间相关性存在渐近方法。在接近这个特征时间时，发现偏离平坦 KPZ 子类，这可以根据相关长度和周长来解释。我们的结果表明，初始曲率的符号在确定 KPZ 类的通用分布和相关函数方面起着关键作用。
