Role of infinite invariant measure in deterministic subdiffusion

Statistical properties of the transport coefficient for deterministic subdiffusion are investigated from the viewpoint of infinite ergodic theory. We find that the averaged diffusion coefficient is characterized by the infinite invariant measure of the reduced map. We also show that when the time di...

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Veröffentlicht in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2010-09, Vol.82 (3 Pt 1), p.030102-030102, Article 030102
Hauptverfasser: Akimoto, Takuma, Miyaguchi, Tomoshige
Format: Artikel
Sprache:eng
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Zusammenfassung:Statistical properties of the transport coefficient for deterministic subdiffusion are investigated from the viewpoint of infinite ergodic theory. We find that the averaged diffusion coefficient is characterized by the infinite invariant measure of the reduced map. We also show that when the time difference is much smaller than the total observation time, the time-averaged mean square displacement depends linearly on the time difference. Furthermore, the diffusion coefficient becomes a random variable and its limit distribution is characterized by the universal law called the Mittag-Leffler distribution.
ISSN:1539-3755
1550-2376
DOI:10.1103/physreve.82.030102