Interacting random walkers

Tobias Ambjörnsson


Tuesday, 20 January 2009, 15:30
Matfys library

The problem of a single random walker has received a lot of attention in science community over the years, the most noteworthy result being that, quite universally, the mean square displacement for such a walker increases linearly with time t. There is now an increasing amount of interest in the problem of INTERACTING random walkers (due to the strong connection of this problem to the fields of, for instance, biophysics, nanofluidics, and cell biology). In particular, the main attention has been on the behaviour of interacting walkers in (quasi)one dimensional systems, so called single-file diffusion. The quantity of main interest in such a system is the mean square displacement of a (fluorescently) tagged particle. It has been found previously (theoretically and experimentally) that the mean square displacement for a tagged particle in a single file system scales as t^(1/2), rather than t as for unconstrained diffusion (in an infinite system). I will explain this result and discuss three new aspects of single-file diffusion: (1) single-file diffusion in finite system (exact solution) (2) a new simple approach to understand the behaviour of single-file type systems (3) single-file diffusion where the particles have different diffusion constants.