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 $\overline{{\delta }^2}$ 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 $\overline{{\delta }^2}$ differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable $\overline{{\delta }^2}$. 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.

4 pages, 4 figures.Article accompanied by a PRL Viewpoint in Physics1, 8 (2008)

References in corpus (4)

• Anomalous dynamics of cell migration
• Probing microscopic origins of confined subdiffusion by first-passage observables
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary

Cited by in corpus (5)

• Pesin-Type Identity for Weak Chaos
• Universal fluctuations in subdiffusive transport
• Helix or Coil? Fate of a Melting Heteropolymer
• Continuous Time Random Walks with Internal Dynamics and Subdiffusive Reaction-Diffusion Equations
• Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes