Brownian motion under intermittent harmonic potentials

We study the effects of an intermittent harmonic potential strength $\mu = \mu_0 \nu$ -- that switches on and off stochastically at a constant rate $\gamma$, overdamped Brownian particle with damping coefficient $\nu$. This can be thought as realistic model for realisation stochastic resetting. show this dynamics admits stationary solution in all parameter regimes compute full time dependent variance position distribution find characteristic relaxation time. exact non-equilibrium state distributions limits (i) $\gamma\ll\mu_0 $ which shows non-trivial distribution, addition $\mu_0\to\infty$, we get back result resetting refractory period; (ii) $\gamma\gg\mu_0$ where relaxes to Boltzmann Ornstein-Uhlenbeck process half original (iii) intermediate $\gamma=2n\mu_0$ $n=1, 2$. The mean first passage (MFPT) target exhibits optimisation switching rate, however unlike instantaneous MFPT does not diverge but reaches value large rates. also similar behavior respect strength. Our results verified experiments colloids using optical tweezers.