TY - JOUR

T1 - Nonergodicity mimics inhomogeneity in single particle tracking

AU - Lubelski, Ariel

AU - Sokolov, Igor M.

AU - Klafter, Joseph

PY - 2008/6/26

Y1 - 2008/6/26

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=46349096647&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.100.250602

DO - 10.1103/PhysRevLett.100.250602

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AN - SCOPUS:46349096647

SN - 0031-9007

VL - 100

JO - Physical Review Letters

JF - Physical Review Letters

IS - 25

M1 - 250602

ER -