Understanding anomalous transport in intermittent maps: From continuous-time random walks to fractalsN. Korabel1, A. V. Chechkin2, R. Klages3, I. M. Sokolov4 and V. Yu. Gonchar2
1 Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Str. 38 D-01187 Dresden, Germany
2 Institute for Theoretical Physics NSC KIPT - Akademicheskaya st. 1 61108 Kharkov, Ukraine
3 School of Mathematical Sciences, Queen Mary, University of London Mile End Road, London E1 4NS, UK
4 Institut für Physik, Humboldt-Universität zu Berlin - Newtonstr. 15 D-12489 Berlin, Germany
received 16 September 2004; accepted in final form 2 February 2005
published online 11 March 2005
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous-time random-walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.
05.45.Ac - Low-dimensional chaos.
05.60.-k - Transport processes.
05.40.Fb - Random walks and Levy flights.
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