Spatial persistence and survival probabilities for fluctuating interfaces

TL;DR

This paper investigates the spatial persistence and survival probabilities of fluctuating interfaces described by KPZ and EW equations, analyzing effects of noise correlations, system size, and sampling distance through numerical and analytical methods.

Contribution

It provides new analytical expressions and numerical verification for the persistence exponents of EW interfaces with correlated noise, and explores the impact of sampling and system size on persistence probabilities.

Findings

Persistence probabilities follow simple scaling laws.

Analytical exponents match numerical results.

Finite sampling affects measured persistence probabilities.

Abstract

We report the results of numerical investigations of the steady-state (SS) and finite-initial-conditions (FIC) spatial persistence and survival probabilities for (1+1)--dimensional interfaces with dynamics governed by the nonlinear Kardar--Parisi--Zhang (KPZ) equation and the linear Edwards--Wilkinson (EW) equation with both white (uncorrelated) and colored (spatially correlated) noise. We study the effects of a finite sampling distance on the measured spatial persistence probability and show that both SS and FIC persistence probabilities exhibit simple scaling behavior as a function of the system size and the sampling distance. Analytical expressions for the exponents associated with the power-law decay of SS and FIC spatial persistence probabilities of the EW equation with power-law correlated noise are established and numerically verified.