Is active motion beneficial for target search with resetting in a thermal environment?

Abstract: Stochastic resetting has recently emerged as an efficient target-searching strategy in various physical and biological systems. The efficiency of this strategy depends on the type of environmental noise, whether it is thermal or telegraphic (active). While the impact of each noise type on a search process has been investigated separately, their combined effects have not been explored. In this work, we explore the effects of stochastic resetting on an active system, namely a self-propelled run-and-tumble particle immersed in a thermal bath. In particular, we assume that the position of the particle is reset at a fixed rate with or without reversing the direction of self-propelled velocity. Using standard renewal techniques, we compute the mean search time of this active particle to a fixed target and investigate the interplay between active and thermal fluctuations. We find that the active search can outperform the Brownian search when the magnitude and flipping rate of self-propelled velocity are large and the strength of environmental noise is small. Notably, we find that the presence of thermal noise in the environment helps reduce the mean first passage time of the run-and-tumble particle compared to the absence of thermal noise. Finally, we observe that reversing the direction of self-propelled velocity while resetting can also reduce the overall search time.