Shortcuts to adiabaticity for Active Brownian Particles

Among the many physical systems exhibiting active behaviour, some have the remarkable property that the degree of activity can be externally controlled. Systems of Janus particles have been realized, for instance, such that the chemical reactions providing self-propulsion are activated by the external light: by tuning the light intensity, it is thus possible to switch the system from a passive-like state to an active phase. The transition is not istantaneous: the thermalization to the final state requires a time that depends on the chosen protocol for the light intensity and the other external parameters, i.e. on the way they are modified in time. It is thus natural to search for "shortcuts to adiabaticity", i.e. protocols bringing the system to the desired final state in a given (short) time interval.

We study this problem analytically for a system of active Brownian particles in two dimensions, whose degree of activity can be externally controlled. Assuming that the particles are confined in a tunable harmonic trap, we present a class of protocols leading from a passive-like to an active-like steady state (and vice-versa) in a controlled way. The minimal time required to complete this kind of transitions is studied as a function of the external parameters, assuming bounds on the stiffness of the external potential.