Local persistence exponent and its log-periodic oscillations

TL;DR

This paper studies how the local persistence exponent of a particle diffusing near self-similar boundaries exhibits log-periodic oscillations, revealing the influence of fractal geometry on diffusion dynamics.

Contribution

It demonstrates through simulations that the persistence exponent shows log-periodic oscillations and analyzes how boundary self-similarity impacts diffusive behavior.

Findings

Persistence exponent exhibits log-periodic oscillations.

Oscillation period and mean value depend on fractal dimension.

Spatial self-similarity influences diffusion and temporal dynamics.

Abstract

We investigate the local persistence exponent of the survival probability of a particle diffusing near an absorbing self-similar boundary. We show by extensive Monte Carlo simulations that the local persistence exponent exhibits log-periodic oscillations over a broad range of timescales. We determine the period and mean value of these oscillations in a family of Koch snowflakes of different fractal dimensions. The effect of the starting point and its local environment on this behavior is analyzed in depth by a simple yet intuitive model. This analysis uncovers how spatial self-similarity of the boundary affects the diffusive dynamics and its temporal characteristics in complex systems.