Laboratoire Matière et Systèmes Complexes

Beyond Brownian motion : Hydrodynamic memory and non-equilibrium dynamics of active agents

Thomas Franosch, Institut für Theoretische Physik, Universität Innsbruck

The pillars of all transport processes have been established in the molecular-kinetic interpretation of diffusion by Einstein and Smoluchowski. The modern formulation is in terms of stochastic differential equations known in the physics community as Langevin equations. In its simplest version they describe a completely overdamped motion where velocities are irrelevant and the dynamics is solely by drift and diffusion. In this presentation I will introduce several model systems where persistent correlations emerge with macroscopic measurable consequences.

First, I discuss the Brownian motion of a suspended mesosized particle in a simple liquid and in particular the emergence of hydrodynamic memory via the coupling to the Navier-Stokes equations. High precision experiments have confirmed these effects for the first time recently and suggest to develop new ultrasensitive biophysical tools.

Next, I investigate the dynamics of a single active particle, i.e. an agent that undergoes self-propelled motion along an axis of orientation which slowly and randomly changes. While the low-order moments of the dynamics are known for quite some time, a complete characterization of the dynamics has been missing so far. Here we show that the intermediate scattering function which corresponds to the moment-generating function can be elaborated analytically and reveals oscillatory behavior for intermediate wave numbers, in striking contrast to passive overdamped systems. We compare our results with recent dynamic differential microscopy measurements and demonstrate that our solution allows reliably extracting motility parameters. Last we briefly discuss the motion of circular swimmers which in addition to the orientational diffusion displays a deterministic drift in the orientation thereby introducing a chirality into the problem.