Nonergodic Behavior of Interacting Bosons in Harmonic Traps

We study the time evolution of a system of interacting bosons in a harmonic trap. In the low-energy regime, the quantum system is not ergodic and displays rather large fluctuations of the ground state occupation number. In the high energy regime of classical physics we find nonergodic behavior for modest numbers of trapped particles. We give two conditions that assure the ergodic behavior of the quantum system even below the condensation temperature.