Laboratoire de Physique Théorique

de la Matière Condensée

Thomas Franosch (Institut für Theoretische Physik, Universität Innsbruck, Austria)

Gravitaxis of a single active particle

The active Brownian particle (ABP) model has become a paradigm for dynamics far from equilibrium and has attracted considerable attention in the statistical-physics/soft-matter community [1,2]. In this model particles undergo directed motion along their axis of orientation which is subject to orientational diffusion. While it is rather easy to simulate the dynamics of such agents in a prescribed potential landscape, analytical progress even for the simplest set-ups has been difficult. Here I present an exact solution for the dynamics of active Brownian particle in a uniform gravitational field as described by the equations of motion of Ref. [3]. We show that the problem maps to the noisy overdamped pendulum or dynamics in a tilted washboard potential. Close to the underlying classical bifurction we unravel a resonance for the diffusion coefficient. We derive the corresponding Fokker-Planck equation and use techniques familiar from quantum mechanics to provide a complete solution. The scaling behavior at the resonance is rationalized in terms of a simple harmonic oscillator picture.

[1] C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).

[2] C. Kurzthaler, C. Devailly, J. Arlt, T. Franosch, W. C. K. Poon, V. A. Martinez, and A. T. Brown, Probing the spatiotemporal dynamics of catalytic janus particles with single-particle tracking and differential dynamic microscopy, Physical Review Letters 121, 078001 (2018).

[3] B. ten Hagen, F. Kümmel, R. Wittkowski, D. Takagi, H. Löwen, and C. Bechinger, Gravitaxis of asymmetric self-propelled colloidal particles, Nature Communications 5, 4829 (2014).