Distribution of zeros in the rough geometry of fluctuating interfaces

ARTURO L. ZAMORATEGUI; VIVIEN LECOMTE; ALEJANDRO B. KOLTON

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

APS

Año: 2016 vol. 93 p. 42118 - 42118

1063-651X

We study numerically the correlations and the distribution of intervals between successive zeros in thefluctuating geometry of stochastic interfaces, described by the Edwards-Wilkinson equation. For equilibriumstates we find that the distribution of interval lengths satisfies a truncated Sparre-Andersen theorem. We showthat boundary-dependent finite-size effects induce nontrivial correlations, implying that the independent intervalproperty is not exactly satisfied in finite systems. For out-of-equilibrium nonstationary states we derive the scalinglaw describing the temporal evolution of the density of zeros starting from an uncorrelated initial condition. Asa by-product we derive a general criterion of the von Neumann?s type to understand how discretization affectsthe stability of the numerical integration of stochastic interfaces. We consider both diffusive and spatiallyfractional dynamics. Our results provide an alternative experimental method for extracting universal informationof fluctuating interfaces such as domain walls in thin ferromagnets or ferroelectrics, based exclusively on the