|
Abstract |
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] Clemens Bechinger, Roberto Di Leonardo, Hartmut Löwen, Charles Reichhardt, Giorgio Volpe, and
Giovanni 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). |
