Abstract
This paper examines the parameter regimes in which coupled atomic and molecular Bose-Einstein condensates do not obey the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional positive-$P$ representation. These equations describe the full quantum state of the coupled condensates and include the commonly used Gross-Pitaevskii equation as the noiseless limit. The model includes all interactions between the particles, background gas losses, two-body losses, and the numerical simulations are performed in three dimensions. It is found that it is possible to differentiate the quantum and semiclassical behavior when the particle density is sufficiently low and the coupling is sufficiently strong.
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