Short-time growth of a Kardar-Parisi-Zhang interface with flat initial conditions

Abstract

The short-time behavior of the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) growth equation with a flat initial condition is obtained from the exact expressions for the moments of the partition function of a directed polymer with one end point 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 or weak-noise limit and describes the universal crossover between the Edwards-Wilkinson and the KPZ universality classes for an initially flat interface.