Abstract. A superposition mechanism for the generation of anomalous diffusion, both subdiffusive and superdiffusive, is established. We consider a general system model in which a probe is tossed into a stochastic bath, and is constantly impacted by random gusts. All gusts affect the probe by a statistically common, yet arbitrary, impact pattern representing the generic gusts–probe interaction. Each gust has its own impact parameters—amplitude, frequency and initiation epoch. The probe's trajectory is the superposition of all gust impacts affecting it. We characterize the class of impact parameter statistics which produce anomalous diffusion probe trajectories for whatever impact patterns applied. This class of 'bath statistics' generates anomalous diffusion in a universal fashion—indifferent to the details of the gusts–probe interaction.

PACS numbers: 05.40.−a, 05.40.Fb, 02.50.−r, 05.40.Ca

Print publication: Issue 47 (27 November 2009)
Received 17 September 2009, in final form 16 October 2009
Published 6 November 2009