Exact short-time height distribution for the flat Kardar-Parisi-Zhang interface

Area of Science:

• * Statistical physics
• * Nonlinear dynamics
• * Surface growth

Background:

• * The Kardar-Parisi-Zhang (KPZ) equation describes the dynamics of growing surfaces.
• * Understanding the height distribution of these surfaces is crucial for characterizing their behavior.
• * Exact solutions for the KPZ equation are rare, especially for short-time dynamics.

Purpose of the Study:

• * To determine the exact short-time height distribution of a 1+1 dimensional KPZ interface with a flat initial condition.
• * To connect the dynamics of flat initial conditions to those of stationary initial conditions.

Main Methods:

• * Employed the optimal fluctuation method.
• * Utilized a time-reversal symmetry specific to the 1+1 dimensional KPZ equation.
• * Incorporated the recently derived exact short-time height distribution for stationary initial conditions.

Main Results:

• * Derived the exact short-time distribution for the one-point height of an evolving 1+1 KPZ interface with a flat initial condition.
• * Identified that the analytic branch of the stationary height distribution's large-deviation function is key.
• * Established a simple mapping: S_{f}(H) = 2^{-3/2}S_{st}(2H), linking flat and stationary initial condition dynamics.

Conclusions:

• * The analytic branch of the stationary initial condition's large-deviation function governs the flat initial condition's short-time height distribution.
• * This finding reveals a deep connection between different initial states in KPZ dynamics.
• * The study provides a significant advancement in understanding the exact statistical properties of the KPZ equation.