Dynamical quantum noise in trapped Bose-Einstein condensates

We introduce the study of dynamical quantum noise in Bose-Einstein condensa tes through numerical simulation of stochastic partial differential equatio ns obtained using phase-space representations. We derive evolution equation s for a single trapped condensate in both the positive-P and Wigner represe ntations and perform simulations to compare the predictions of the two meth ods. The positive-P approach is found to be highly susceptible to the stabi lity problems that have been observed in other strongly nonlinear, weakly d amped systems. Using the Wigner representation, we examine the evolution of several quantities of interest using from a variety of choices of initial stare for the condensate and compare results to those for single-mode model s. [S1050-2947(98)06612-8].