Oliveira T J, Alves S G, Ferreira S C
Departamento de Física, Universidade Federal de Viçosa, 36570-000 Viçosa, Minas Gerais, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Apr;87(4):040102. doi: 10.1103/PhysRevE.87.040102. Epub 2013 Apr 22.
The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different from their Tracy-Widom counterpart in one dimension, were found. Distributions exhibit finite-time corrections hallmarked by a shift in the mean decaying as t(-β), where β is the growth exponent. Our results support a generalization of the ansatz h=v(∞)t+(Γt)(β)χ+η+ζt(-β) to higher dimensions, where v(∞), Γ, ζ, and η are nonuniversal quantities whereas β and χ are universal and the last one depends on the surface geometry. Generalized Gumbel distributions provide very good fits of the distributions in at least four orders of magnitude around the peak, which can be used for comparisons with experiments. Our numerical results call for analytical approaches and experimental realizations of the KPZ class in two-dimensional systems.
通过考虑平面和曲面几何的广泛模拟，在2 + 1维中研究了属于 Kardar - Parisi - Zhang（KPZ）普适类的模型的动力学机制。发现了与一维中 Tracy - Widom 分布不同的依赖于几何的普适分布。分布表现出有限时间修正，其特征是均值的偏移按 t^(-β)衰减，其中β是增长指数。我们的结果支持将假设 h = v(∞)t + (Γt)^(β)χ + η + ζt^(-β)推广到更高维度，其中 v(∞)、Γ、ζ 和 η 是非普适量，而β和χ是普适的，且最后一个依赖于表面几何。广义 Gumbel 分布在峰值周围至少四个数量级上对分布提供了非常好的拟合，可用于与实验进行比较。我们的数值结果呼吁对二维系统中的 KPZ 类进行解析方法和实验实现。
