title: Random time-scale invariant diffusion and transport coefficients.
abstract: Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement delta2[over ] 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 delta2[over ] differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable delta2[over ]. 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.
authors.affiliation: Department of Physics, Bar Ilan University, Ramat-Gan, Israel.
authors.forename: Y
authors.initials: Y
authors.lastname: He
authors.forename: S
authors.initials: S
authors.lastname: Burov
authors.forename: R
authors.initials: R
authors.lastname: Metzler
authors.forename: E
authors.initials: E
authors.lastname: Barkai