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arXiv · 0807.4793

Random Time-Scale Invariant Diffusion and Transport Coefficients

Y. He·S. Burov·R. Metzler·E. Barkai
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Abstract

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement $\overline{δ^2}$ of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that $\overline{δ^2}$ differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable $\overline{δ^2}$. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.

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Y. He, S. Burov, R. Metzler, E. Barkai. 2008-07-30. Random Time-Scale Invariant Diffusion and Transport Coefficients. https://doi.org/10.1103/physrevlett.101.058101

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