Dynamics of self-propelled particles over a periodic potential landscape

We report a systematic study of self-propelled particles (SPPs) over a periodic potential landscape. A microgroove-patterned polydimethylsiloxane (PDMS) substrate is constructed using the techniques of photolithography and thermal imprinting to provide a gravitational potential landscape $U_0(x)$ for a monolayer of diffusing SPPs. The effective potential $U(x)$ is obtained from the measured population probability histogram $P(x)$ of the SPPs at varying activity levels. Our work provides a physical understanding on how the propulsion speed of SPPs affects the effective potential using the fixed angle approximation. With this understanding, one can reconstruct the equilibrium potential $U_0(x)$ from the measured $U(x)$. It is found that the histogram of dwell time has an exponential distribution and the mean dwell time follows a Kramers-like equation. This work demonstrates a useful experimental system to quantitatively study SPPs in an external potential field.