Universal fluctuations in subdiffusive transportI. M. Sokolov1, E. Heinsalu2, 3, P. Hänggi4 and I. Goychuk4
1 Institut für Physik, Humboldt-Universität zu Berlin - Newtonstraße 15, D-12489 Berlin, Germany
2 National Institute of Chemical Physics and Biophysics - Rävala 10, Tallinn 15042, Estonia
3 IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB) - E-07122 Palma de Mallorca, Spain
4 Institut für Physik, Universität Augsburg - Universitätsstr. 1, D-86135 Augsburg, Germany
received 5 February 2009; accepted in final form 20 April 2009; published May 2009
published online 22 May 2009
Subdiffusive transport in tilted washboard potentials is investigated within the fractional Fokker-Planck equation approach by making reference to the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law. The latter is defined by the index of subdiffusion and the mean subvelocity only. Interestingly this law depends neither on the size of the system or measurement time, nor on the bias strength or on the specific form of the washboard potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical reasoning are corroborated by Monte Carlo simulations of the underlying CTRW.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
05.40.Fb - Random walks and Levy flights.
02.50.-r - Probability theory, stochastic processes, and statistics.
© EPLA 2009