Harmonically Trapped Classical Gas under Critical Rotation

We study one- and two-dimensional systems of two interacting particles in a time dependent harmonic potential. In a case of one-dimensional geometry a frequency of the potential varies periodically, while in the two-dimen- sional case the harmonic potential rotates with a constant angular velocity. We show that depending on the driving frequency the distance between the particles can either explode or stay bound. Repulsive interaction can prevent the explosion, which seems quite counter-intuitive. Our work is related to Ecole Normale Superieure experiment and shows that the effect found there is purely classical.