Applied Mathematics seminar | Ralf Metzler, What Einstein Did Not Know: Anomalous Diffusion, Ageing, and Ergodicity Breaking

Single particle trajectories are measured routinely in a large variety of systems on many scales, including the motion of single molecules in living biological cells, the motion of humans or animals, or the transport of rocks in mountain streams. Often the dynamics of the measured particles deviate from the laws of standard, Einsteinian diffusion. Such anomalous diffusion poses subtle problems to the physical interpretation of the measured single trajectories and their evaluation in terms of time averages. Indeed, in many cases the time averages of the motion deviate from the known ensemble averages, a violation of ergodicity in the Boltzmann sense. In this talk it will be shown that the behaviour of time averaged observables such as the mean squared displacement often defy our intuition, and how new tools in stochastic analysis help us to properly understand measured data.

Reference:

E Barkai, Y Garini, and R Metzler, Physics Today 65(8), 29 (2012).