Short time growth of a KPZ interface with flat initial conditions

Thomas Gueudre 1, Pierre Le Doussal 1, Alberto Rosso 2, Adrien Henry 2, Pasquale Calabrese 3

Physical Review E 86 (2012) 041151

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.

  • 1. Laboratoire de Physique Théorique de l'ENS (LPTENS),
    CNRS : UMR8549 – Université Paris VI - Pierre et Marie Curie – Ecole Normale Supérieure de Paris - ENS Paris
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. Dipartimento di Fisica dell'Universita di Pisa and INFN,Pisa,
    UNIVERSITÀ DEGLI STUDI DI PISA