  A full treatment of decoherence and dephasing effects in BEC interferometry
has been developed based on using quantum correlation functions for treating
interferometric effects. The BEC is described via a phase space distribution
functional of the Wigner type for the condensate modes and the positive P type
for the non-condensate modes. Ito equations for stochastic condensate and
non-condensate field functions replace the functional Fokker-Planck equation
for the distribution functional and stochastic averages of field function
products determine the quantum correlation functions.
