English

Competing Universalities in Kardar-Parisi-Zhang (KPZ) Growth Models

Statistical Mechanics 2019-02-15 v1

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)