Volume 70, Number 1, April 2005
|Page(s)||63 - 69|
|Published online||11 March 2005|
Understanding anomalous transport in intermittent maps: From continuous-time random walks to fractals
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
Accepted: 2 February 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.
PACS: 05.45.Ac – Low-dimensional chaos / 05.60.-k – Transport processes / 05.40.Fb – Random walks and Levy flights
© EDP Sciences, 2005
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