  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 behaviour when the particle density is sufficiently low and the
coupling is sufficiently strong.
