##
Interacting random walkers

### Tobias Ambjörnsson

MIT

**Tuesday, 20 January 2009, 15:30**

Matfys library

**Abstract**:

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.