Kardar-Parisi-Zhang Interfaces with Inward Growth

TL;DR

This study investigates inward-growing KPZ interfaces from ring initial conditions, revealing they follow flat subclass statistics initially, with deviations near a characteristic time, highlighting the importance of initial curvature sign.

Contribution

It introduces a holography-based method to experimentally realize arbitrary initial conditions and demonstrates the impact of initial curvature sign on KPZ universality class behavior.

Findings

Inward KPZ interfaces initially follow flat subclass distributions.

Deviations occur near a characteristic time related to initial curvature.

The initial curvature sign critically influences universal distribution and correlations.

Abstract

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 $\text{Airy}_1$ 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.