2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147569We present a quantum theory of low-lying excitations in a trapped Bose condensate with finite particle numbers. We find that even at zero temperature condensate number fluctuations and/or fluctuations of the excitation frequency due to quantum uncertainties of the mode occupation lead to a collapse of the collective modes due to dephasing. Coherent revivals of the collective excitations are predicted on a much longer timescale. Depletion of collective modes due to second-harmonic generation is discussed.final version published in Phys.Rev.A (1997)Condensed Mattertext