Marco Baldovin (U. Paris-Saclay)
Control of Active Brownian Particles: An exact solution
Control of stochastic systems is a challenging open problem in statistical physics, with a wealth of potential applications from biology to granulates. Given a system whose stochastic dynamics is ruled by an externally-tunable driving parameter, the goal is to find protocols for the control that allow the system to reach a target state in a given finite time. Unlike most cases investigated so far, we aim here at controlling a genuinely out-of-equilibrium system, the two dimensional Active Brownian Particles model with harmonic confinement, a paradigm for the study of self-propelled bacteria.
Inspired by experiments where the activity of the particles and the stiffness of the confining potential can be controlled in time, we search for protocols for these driving parameters. We aim at bringing the system from an initial passive-like steady state, where the qualitative behavior of the particle is similar to that of a passive colloid, to a final active-like one, characterized by a strongly out-of-equilibrium position distribution. The optimization of the transition time is investigated in the case of bounded stiffness.