Iddo Eliazar and Joseph Klafter 2009 J. Phys. A: Math. Theor. 42 472003 doi:10.1088/1751-8113/42/47/472003
On the generation of anomalous diffusion
FREE ARTICLEIddo Eliazar1 and Joseph Klafter2,3
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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
- MSC
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60G50 Sums of independent random variables; random walks
60J60 Diffusion processes (See also 58J65)
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) (See also 60H10)
60J65 Brownian motion (See also 58J65)
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. (See also 60G50)
- Subjects
- Dates
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Issue 47 (27 November 2009)
Received 17 September 2009, in final form 16 October 2009
Published 6 November 2009
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On the generation of anomalous diffusion
Iddo Eliazar and Joseph Klafter 2009 J. Phys. A: Math. Theor. 42 472003
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