  We sketch the major steps in a functional integral derivation of a new set of
Stochastic Gross-Pitaevsky equations (GPE) for a Bose-Einstein condensate (BEC)
confined to a trap at zero temperature with the averaged effects of
non-condensate modes incorporated as stochastic sources. The closed-time-path
(CTP) coarse-grained effective action (CGEA) or the equivalent influence
functional method is particularly suitable because it can account for the full
back-reaction of the noncondensate modes on the condensate dynamics
self-consistently. The Langevin equations derived here containing nonlocal
dissipation together with colored and multiplicative noises are useful for a
stochastic (as distinguished from say, a kinetic) description of the
nonequilibrium dynamics of a BEC. This short paper contains original research
results not yet published anywhere.
