Collapses and Revivals of Collective Excitations in Trapped Bose   Condensates
  We 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. 
R. Graham (Universit"at GH Essen), D.F. Walls and M.J. Collett   (University of Auckland), M. Fliesser (Universit"at GH Esse...