Short time growth of a KPZ interface with flat initial conditions

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.

9 pages, 7 figures

References in corpus (24)

• Level-Spacing Distributions and the Airy Kernel
• Shape Fluctuations and Random Matrices
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• The one-dimensional KPZ equation: an exact solution and its universality
• Burgers Turbulence
• Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
• Free-energy distribution of the directed polymer at high temperature
• Growing interfaces uncover universal fluctuations behind scale invariance
• Exact scaling functions for one-dimensional stationary KPZ growth
• Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
• An exact solution for the KPZ equation with flat initial conditions
• Exact height distributions for the KPZ equation with narrow wedge initial condition
• Exact solution for the stationary Kardar-Parisi-Zhang equation
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Correlation functions of the one-dimensional attractive Bose gas
• The crossover regime for the weakly asymmetric simple exclusion process
• Polynuclear growth on a flat substrate and edge scaling of GOE eigenvalues
• Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
• Dynamics of the attractive 1D Bose gas: analytical treatment from integrability
• The height distribution of the KPZ equation with sharp wedge initial condition: numerical evaluations
• Replica approach to the KPZ equation with half Brownian motion initial condition
• Attempted Bethe ansatz solution for one-dimensional directed polymers in random media
• The universal high temperature regime of pinned elastic objects

Cited by in corpus (24)

• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Large Deviations of Surface Height in the Kardar-Parisi-Zhang Equation
• Exact short-time height distribution in 1D KPZ equation and edge fermions at high temperature
• Directed polymer near a hard wall and KPZ equation in the half-space
• Exact short-time height distribution in 1D KPZ equation with Brownian initial condition
• Short-time height distribution in 1d KPZ equation: starting from a parabola
• Interaction quench in a Lieb-Liniger model and the KPZ equation with flat initial conditions
• Landau theory of the short-time dynamical phase transitions of the Kardar-Parisi-Zhang interface
• Simple derivation of the $(-\lambda H{)}^{5/2}$ tail for the 1D KPZ equation
• Exact short-time height distribution for the flat Kardar-Parisi-Zhang interface
• Diffusion in time-dependent random media and the Kardar-Parisi-Zhang equation
• From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation
• Finite-size effects in the short-time height distribution of the Kardar-Parisi-Zhang equation
• Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation
• Probing the large deviations of the Kardar-Parisi-Zhang equation at short time with an importance sampling of directed polymers in random media
• Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
• Observing symmetry-broken optimal paths of stationary Kardar-Parisi-Zhang interface via a large-deviation sampling of directed polymers in random media
• Time-averaged height distribution of the Kardar-Parisi-Zhang interface
• The circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer
• Static fluctuations of a thick 1D interface in the 1+1 Directed Polymer formulation: numerical study
• Nonlocal Asymmetric exclusion process on a ring and conformal invariance
• Crossover between various initial conditions in KPZ growth: flat to stationary
• Exact short-time height distribution and dynamical phase transition in the relaxation of a Kardar-Parisi-Zhang interface with random initial condition
• Analytical Methods and Field Theory for Disordered Systems