Langevin equation of collective modes of Bose-Einstein condensates in   traps
  A quantum Langevin equation for the amplitudes of the collective modes in Bose-Einstein condensate is derived. The collective modes are coupled to a thermal reservoir of quasi-particles, whose elimination leads to the quantum Langevin equation. The dissipation rates are determined via the correlation function of the fluctuating force and are evaluated in the local-density approximation for the spectrum of quasi-particles and the Thomas-Fermi approximation for the condensate. I take great pleasure in dedicating this paper to Gregoire Nicolis on the occasion of his sixtieth birthday. 
Robert Graham (Fachbereich Physik, Universit\"at-Gesamthochschule   Essen, Germany)