  A Langevin equation for the complex amplitude of a single-mode Bose-Einstein
condensate 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 are
thereby derived and evaluated for simple trap geometries, a cubic box with
cyclic boundary conditions and an isotropic parabolic trap. The number
fluctuations in the condensate, their correlation time, and the
temperature-dependent collapse-time of the order parameter as well as its
phase-diffusion coefficient are calculated.
