Short time growth of a KPZ interface with flat initial conditions

TL;DR

This paper derives exact short time expansions for the KPZ interface height with flat initial conditions, revealing the universal crossover from Edwards-Wilkinson to KPZ behavior, validated by high-precision simulations.

Contribution

It provides the first exact short time cumulant expansions for the KPZ equation with flat initial conditions, connecting theoretical predictions with numerical results.

Findings

Exact short time cumulant expansions derived

Universal crossover between Edwards-Wilkinson and KPZ confirmed

High-precision simulations validate theoretical results

Abstract

The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other fixed. From these expressions, the short time expansions of the lowest cumulants of the KPZ height field are exactly derived. The results for these two classes of cumulants are checked in high precision lattice numerical simulations. The short time limit considered here is relevant for the study of the interface growth in the large diffusivity/weak noise limit, and describes the universal crossover between the Edwards-Wilkinson and KPZ universality classes for an initially flat interface.