Noninteracting particles in a harmonic trap with a stochastically driven center

We study a system of N noninteracting particles on a line in the presence of a harmonic trap , where the trap center z(t) undergoes a stochastic modulation that remains bounded in time. We show that this stochastic modulation drives the system into a nonequilibrium stationary state, where the joint distribution of the positions of the particles is not factorizable. This indicates strong correlations between the positions of the particles that are not inbuilt, but rather get generated by the dynamics itself. Moreover, we show that the stationary joint distribution can be fully characterized and has a special conditionally independent and identically distributed structure. This special structure allows us to compute several observables analytically even in such a strongly correlated system, for an arbitrary drive z(t) that remains bounded in time. These observables include the average density profile, the correlations between particle positions, the order and gap statistics, as well as the full counting statistics. We then apply our general results to two specific examples where (i) z(t) represents a dichotomous telegraphic noise, and (ii) z(t) represents an Ornstein–Uhlenbeck process. Our analytical predictions are verified in numerical simulations, finding excellent agreement.