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Anomalous diffusion with log-periodic modulation in a selected time interval
L Padilla1, H O Mártin, J L Iguain
1Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR) and Departamento de Física FCEyN, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina. lorenapadilla.r@gmail.com
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.
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