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Condensed Matter > Statistical Mechanics

arXiv:1304.5577 (cond-mat)
[Submitted on 20 Apr 2013 (v1), last revised 25 Jun 2013 (this version, v2)]

Title:Distributional Ergodicity in Stored-Energy-Driven Lévy Flights

Authors:Takuma Akimoto, Tomoshige Miyaguchi
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Abstract:We study a class of random walk, the stored-energy-driven Lévy flight (SEDLF), whose jump length is determined by a stored energy during a trapped state. The SEDLF is a continuous-time random walk with jump lengths being coupled with the trapping times. It is analytically shown that the ensemble-averaged mean square displacements exhibit subdiffusion as well as superdiffusion, depending on the coupling parameter. We find that time-averaged mean square displacements increase linearly with time and the diffusion coefficients are intrinsically random, a manifestation of {\it distributional ergodicity}. The diffusion coefficient shows aging in subdiffusive regime, whereas it increases with the measurement time in superdiffusive regime.
Comments: 7 pages, 6 figures
Subjects: Statistical Mechanics (cond-mat.stat-mech); Probability (math.PR)
Cite as: arXiv:1304.5577 [cond-mat.stat-mech]
  (or arXiv:1304.5577v2 [cond-mat.stat-mech] for this version)
  https://doi.org/10.48550/arXiv.1304.5577
Journal reference: Phys. Rev. E 87, 062134 (2013)
Related DOI: https://doi.org/10.1103/PhysRevE.87.062134

Submission history

From: Takuma Akimoto [view email]
[v1] Sat, 20 Apr 2013 01:45:43 UTC (844 KB)
[v2] Tue, 25 Jun 2013 01:46:43 UTC (1,258 KB)
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