Competing Universalities in Kardar-Parisi-Zhang (KPZ) Growth Models
Abstract
We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) 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 (TW) distribution for p<0.5, and to the Gaussian unitary ensemble TW 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.
Keywords
Cite
@article{arxiv.1901.05716,
title = {Competing Universalities in Kardar-Parisi-Zhang (KPZ) Growth Models},
author = {Abbas Ali Saberi and Hor Dashti-N. and Joachim Krug},
journal= {arXiv preprint arXiv:1901.05716},
year = {2019}
}
Comments
5 pages, 6 figures, Phys. Rev. Lett. (2019) (accepted)