Journal
PHYSICAL REVIEW LETTERS
Volume 100, Issue 25, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.100.250602
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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 similar to T alpha-1 which depends on the length of the trajectory T.
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