Department of Physics, University of Tehran, P.O. Box 14395-547, Tehran, Iran.
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.
Phys Rev Lett. 2019 Feb 1;122(4):040605. doi: 10.1103/PhysRevLett.122.040605.
We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang interfaces with curved and flat initial conditions. We introduce a control parameter p as the probability for the initially flat geometry to be chosen and compute the phase diagram as a function of p. We find that the distribution of the fluctuations converges to the Gaussian orthogonal ensemble Tracy-Widom distribution for p<0.5, and to the Gaussian unitary ensemble Tracy-Widom distribution for p>0.5. For p=0.5 where the two geometries are equally weighted, the behavior is governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a phenomenological theory to explain our findings and discuss possible applications in nonequilibrium transport and traffic flow.
我们报告了在具有弯曲和平坦初始条件的两个相互作用的（1+1）-维 Kardar-Parisi-Zhang 界面交叉点处高度波动的普遍性。我们引入控制参数 p 作为初始平坦几何被选择的概率，并计算作为 p 的函数的相图。我们发现，对于 p<0.5，波动的分布收敛到高斯正交系综 Tracy-Widom 分布，而对于 p>0.5，波动的分布收敛到高斯酉系综 Tracy-Widom 分布。对于 p=0.5，两种几何形状的权重相等，行为由 Brownian 运动的普遍类别的突发高斯统计量控制。我们提出了一个唯象理论来解释我们的发现，并讨论了在非平衡输运和交通流中的可能应用。
