title: Fractional kinetics emerging from ergodicity breaking in random media.
abstract: We present a modeling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single-particle tracking experiments in living cells, such as ergodicity breaking, p variation, and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.
authors.affiliation: BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain.
authors.forename: Daniel
authors.initials: D
authors.lastname: Molina-García
authors.affiliation: BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain.|Department of Theoretical Physics, Belgorod National Research University, 14 Studencheskaya, 308015 Belgorod, Russia.
authors.forename: Tuan Minh
authors.initials: TM
authors.lastname: Pham
authors.affiliation: BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain.|ISTI-CNR, Istituto di Scienza e Tecnologie dell'Informazione "A. Faedo," Via Moruzzi 1, I-56124 Pisa, Italy.
authors.forename: Paolo
authors.initials: P
authors.lastname: Paradisi
authors.affiliation: ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
authors.forename: Carlo
authors.initials: C
authors.lastname: Manzo
authors.affiliation: BCAM - Basque Center for Applied Mathematics, Alameda de Mazarredo 14, E-48009 Bilbao, Basque Country, Spain.|Ikerbasque - Basque Foundation for Science, Calle de Mará Díaz de Haro 3, E-48013 Bilbao, Basque Country, Spain.
authors.forename: Gianni
authors.initials: G
authors.lastname: Pagnini