Europhys. Lett., 70 (1), pp. 63-69 (2005)
DOI: 10.1209/epl/i2004-10460-6

Understanding anomalous transport in intermittent maps: From continuous-time random walks to fractals

N. Korabel¹, A. V. Chechkin², R. Klages³, I. M. Sokolov⁴ and V. Yu. Gonchar<sup>2

1</sup>  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

Abstract
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