Anomalous transport and diffusion of coupled Brownian
particles with periodic driving forces
Ying Wang1, Chunhua Zeng1,a, Bao-Quan Ai2,b
1 Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China
2 Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, GPETR Center
for Quantum Precision Measurement, SPTE, South China Normal University, Guangzhou 510006, China
Received: 28 June 2021 / Accepted: 29 September 2021
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany,
part of Springer Nature 2021
Abstract Transport and diffusion of coupled Brownian particles in a spatially periodic potential are investigated under a constant biased force and two periodic driving forces. The
impact of the periodic driving forces on the transport characteristics of coupled particles is
discussed by Brownian dynamic simulation methods. The force–velocity relation which has
been described for the coupled particles displays complex and rich behaviors, including absolute, nonlinear and differential negative mobilities. When the particle number or the coupled
strength between particles increases, the anomalous transport and multiple current reversals will gradually disappear. In addition, we analyze anomalous diffusions (subdiffusion,
superdiffusion and hyperdiffusion) corresponding to these anomalous mobilities. Meanwhile,
we discuss physical mechanisms behind these findings via the mean square displacement,
the probability distribution of the velocity and mobility coefficient of the coupled particles.
Our results may contribute to further understanding of peculiar transport phenomena in the
microworld.

a e-mail: zchh2009@126.com (corresponding author)
b e-mail: aibq@scnu.edu.cn (corresponding author)

Eur. Phys. J. Plus (2021) 136:1071
https://doi.org/10.1140/epjp/s13360-021-02047-x