Inertia effects in the spatial distribution and dynamics of active particles with space-dependent activity

The activity of particles can be modulated by external conditions such as light irradiation. Research on active particles with spatially varying activity has demonstrated that active particles tend to accumulate in low-activity regions and form a polarity layer at the interface, directed from the high-activity to the low-activity region. Here, we investigate the distribution and dynamics of individual or an ideal gas of inertial particles in a space with alternating active and passive regions. Our findings reveal that high inertia leads to a pronounced depletion layer in the passive region. At the interface between the active and passive regions, in addition to the usual polarity layer, an adjacent anti-polarity layer forms on the active-region side. In extreme situations (narrow region width and long persistence times), the interfacial polarity layer can even reverse orientation. Dynamically, we observe long-time peaks in the velocity autocorrelation function of particles within the active region. For particles with high inertia, the peak can even exceed 1. Correspondingly, the mean squared displacement of high-inertia particles in the active region exhibits an unusual superdiffusive behavior (∼t3). In addition, kinetic temperature and pressure differences arise between the active and passive regions. The effective temperature of particles with high inertia exhibits a gradual gradient across the active region. Our study provides new insights into the behavior of inertial active particles under spatially modulated activity and lays the groundwork for further exploration of their collective behaviors when interactions are included.