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. . 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.
 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).
 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).
 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).