Takuma Akimoto, Tomoshige Miyaguchi
We introduce a new class of random walk, the stored-energy-driven L\'evy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a novel type of anomalous diffusion, including the usual continuous-time random walk as a spacial case. We show that the ensemble-averaged mean square displacements exhibit subdiffusion as well as superdiffusion, depending on a parameter. We find that the diffusion coefficients of time-averaged mean square displacements are intrinsically random, a manifestation of distributional ergodicity. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.
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http://arxiv.org/abs/1304.5577
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