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 disp
lays rather large fluctuations of the ground-state occupation number. In th
e high-energy regime of classical physics we find nonergodic behavior for m
odest numbers of trapped particles. We give two conditions that assure the
ergodic behavior of the quantum system even below the condensation temperat
ure. [S1050-2947(98)08512-0].