Directional transport of active particles in the two-dimensional asymmetric ratchet potential field

Abstract

Relationship between matter and energy transport has always been one of the key issues that researchers have been searching for in statistical physics and complexity science. In many transport phenomena, the active transport with zero or even no external force in life activities has attracted extensive attention of scholars. As a special kind of active particles, active Brownian particles have received the attention of physicists and biophysicists. These active particles are natural or artificially designed particles, whose scale is in the order of micrometer or nanometer. Different from the traditional passive Brownian particles driven by the equilibrium heat wave generated by the random collision of the surrounding fluid molecules, active Brownian particles can extract energy from their own environment to drive their own motion. Here, directional transport process of active particles in the two-dimensional asymmetric ratchet potential field is analyzed. Both the overdamped medium and the critically damped one are emphasized. Langevin equations with inertia term are introduced to describe the impacts of the self-driven force, friction coefficient, etc. on the directional motion. Then, the average particle speed is found. Thereafter, the relationships between the speed and critical parameters like self-driven force, friction coefficient, etc. are obtained. Two different dynamical domination mechanisms are found, which are expressed as the random collision domination and the self-driven force domination, respectively. Furthermore, the random collision domination is found to correspond to the much higher peak of the two-dimensional asymmetric Brownian rachet potential field, while the self-driven force domination is found to correspond to the much lower peak of the introduced potential. The study will be helpful for discovering the stochastic thermodynamics mechanisms in nonlinear dynamics and nonlinear properties of such multibody interaction system in statistical physics and complex system science.