title: Intrinsic randomness of transport coefficient in subdiffusion with static disorder.
abstract: Fluctuations in the time-averaged mean-square displacement for random walks on hypercubic lattices with static disorder are investigated. It is analytically shown that the diffusion coefficient becomes a random variable as a manifestation of weak ergodicity breaking. For two- and higher- dimensional systems, the distribution function of the diffusion coefficient is found to be the Mittag-Leffler distribution, which is the same as for the continuous-time random walk, whereas for one-dimensional systems a different distribution (a modified Mittag-Leffler distribution) arises. We also present a comparison of these two distributions in terms of an ergodicity-breaking parameter and show that the modified Mittag-Leffler distribution has a larger deviation from ergodicity. Some remarks on similarities between these results and observations in biological experiments are presented.
authors.affiliation: Department of Applied Physics, Osaka City University, Osaka 558-8585, Japan. tomo@a-phys.eng.osaka-cu.ac.jp
authors.forename: Tomoshige
authors.initials: T
authors.lastname: Miyaguchi
authors.forename: Takuma
authors.initials: T
authors.lastname: Akimoto
mesh_terms: D000465:Algorithms; D000818:Animals; D001692:Biological Transport; D001703:Biophysics / Q000379:methods*; D002467:Cell Nucleus / Q000378:metabolism; D003198:Computer Simulation; D004247:DNA / Q000737:chemistry*; D004058:Diffusion; D004926:Escherichia coli / Q000378:metabolism*; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D016615:Telomere / Q000378:metabolism; D013997:Time Factors
chemical_list: D004247:DNA