Anomalous diffusion with log-periodic modulation in a selected time interval

TL;DR

This paper investigates how disorder affects anomalous diffusion with log-periodic modulation on self-similar substrates, showing that disorder can suppress or localize oscillations while preserving subdiffusive behavior.

Contribution

It analytically and numerically demonstrates how disorder influences log-periodic oscillations and subdiffusion in self-similar systems, revealing conditions for their suppression or localization.

Findings

Disorder can wash out oscillations in self-similar random walks.

Subdiffusive behavior persists despite disorder.

Oscillations can be localized within specific time intervals.

Abstract

On certain self-similar substrates the time behavior of a random walk is modulated by logarithmic periodic oscillations on all time scales. We show that if disorder is introduced in a way that self-similarity holds only in average, the modulating oscillations are washed out but subdiffusion remains as in the perfect self-similar case. Also, if disorder distribution is appropriately chosen the oscillations are localized in a selected time interval. Both the overall random walk exponent and the period of the oscillations are analytically obtained and confirmed by Monte Carlo simulations.