Nonergodicity mimics inhomogeneity in single particle tracking

Ariel Lubelski*, Igor M. Sokolov, Joseph Klafter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 ψ(t) t-1-α, with 0<α<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 Keff∼Tα-1 which depends on the length of the trajectory T.

Original languageEnglish
Article number250602
JournalPhysical Review Letters
Issue number25
StatePublished - 26 Jun 2008


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