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 |
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| container_end_page | 030102 |
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| container_issue | 3 Pt 1 |
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| container_title | Physical review. E, Statistical, nonlinear, and soft matter physics |
| container_volume | 82 |
| creator | Akimoto, Takuma Miyaguchi, Tomoshige |
| description | 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. |
| doi_str_mv | 10.1103/physreve.82.030102 |
| format | Article |
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| ispartof | Physical review. E, Statistical, nonlinear, and soft matter physics, 2010-09, Vol.82 (3 Pt 1), p.030102-030102, Article 030102 |
| issn | 1539-3755 1550-2376 |
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| source | American Physical Society Journals |
| title | Role of infinite invariant measure in deterministic subdiffusion |
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