title: Nonergodicity mimics inhomogeneity in single particle tracking.
abstract: Most statistical theories of anomalous diffusion rely on ensemble-averaged quantities such as the mean squared displacement. Single molecule tracking measurements require, however, temporal averaging. We contrast the two approaches in the case of continuous-time random walks with a power-law distribution of waiting times psi(t) proportional to t{-1-alpha}, with 0<alpha<1, lacking the mean. We show that, contrary to what is expected, the temporal averaged mean squared displacement leads to a simple diffusive behavior with diffusion coefficients that strongly differ from one trajectory to another. This distribution of diffusion coefficients renders a system inhomogeneous: an ensemble of simple diffusers with different diffusion coefficients. Taking an ensemble average over these diffusion coefficients results in an effective diffusion coefficient K{eff} approximately T{alpha-1} which depends on the length of the trajectory T.
authors.affiliation: School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv 69978, Israel.
authors.forename: Ariel
authors.initials: A
authors.lastname: Lubelski
authors.forename: Igor M
authors.initials: IM
authors.lastname: Sokolov
authors.forename: Joseph
authors.initials: J
authors.lastname: Klafter