Volume 93, Number 2, March 2011
|Number of page(s)||6|
|Published online||02 February 2011|
Markovian embedding of fractional superdiffusion
Institute of Physics, University of Augsburg - Universitätsstraß e 1, D-86135 Augsburg, Germany
Accepted: 4 January 2011
The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized Brownian Motion with long time persistence (superdiffusion), or anti-persistence (subdiffusion) of both velocity-velocity correlations, and position increments. It presents a case of the Generalized Langevin Equation (GLE) with a singular power law memory kernel. We propose and numerically realize a numerically efficient and reliable Markovian embedding of this superdiffusive GLE, which accurately approximates the FLE over many, about r = N log10 b − 2, time decades, where N denotes the number of exponentials used to approximate the power law kernel, and b>1 is a scaling parameter for the hierarchy of relaxation constants leading to this power law. Besides its relation to the FLE, our approach presents an independent and very flexible route to model anomalous diffusion. Studying such a superdiffusion in tilted washboard potentials, we demonstrate the phenomenon of transient hyperdiffusion which emerges due to transient kinetic heating effects.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 87.16.Uv – Active transport processes / 02.50.-r – Probability theory, stochastic processes, and statistics
© EPLA, 2011
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.