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A Langevin equation for the complex amplitude of a single-mode Bose-Einsteincondensate is derived. The equation is first formulated phenomenologically,defining three transport parameters. It is then also derived microscopically.Expressions for the transport parameters in the form of Green-Kubo formulas arethereby derived and evaluated for simple trap geometries, a cubic box withcyclic boundary conditions and an isotropic parabolic trap. The numberfluctuations in the condensate, their correlation time, and thetemperature-dependent collapse-time of the order parameter as well as itsphase-diffusion coefficient are calculated.Comment: 29 pages, Revtex, to appear in Phys.Rev.

Condensate fluctuations in finite Bose-Einstein condensates at finite temperature