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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] 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). |
