Abstract

Exceptional venue: MR13

In many situations of physical or biological interest, one encounters the situation where a tracer particle diffuses in a crowded environment. This is exemplified by the diffusion of active macromolecules or organelles in the intracellular medium, or by microrheology experiments. In those situations, the interactions between the tracer particle and its environment give rise to correlations which control the dynamics of the tracer, and whose determination is generally a major challenge. Among the different theoretical strategies that were employed to describe tracer diffusion in crowded environments, the study of hardcore lattice gases has been particularly fruitful. These models, which are also called exclusion processes, have progressively become central in nonequilibrium statistical mechanics.

I will first present results on the diffusion coefficient of an active tracer on a 2D lattice. Starting from the master equation of the problem, we put forward a closure approximation which is accurate for a very wide range of parameters, and that correctly captures different nonequilibrium effects, which are the signature of the activity in the system. I will then focus on the particular case of the one-dimensional geometry. This situation is often referred to as “single-file transport”, and is a fundamental model for the tracer subdiffusion observed experimentally in confined systems. I will present a number of exact results on the statistics of the position of a passive tracer and on the correlations between the tracer and its environment.