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We study the dynamics of a two-mode Bose-Einstein condensate in the vicinityof a mean-field dynamical instability. Convergence to mean-field theory (MFT),with increasing total number of particles $N$, is shown to be logarithmicallyslow. Using a density matrix formalism rather than the conventionalwavefunction methods, we derive an improved set of equations of motion for themean-field plus the fluctuations, which goes beyond MFT and provides accuratepredictions for the leading quantum corrections and the quantum break time. Weshow that the leading quantum corrections appear as decoherence of the reducedsingle-particle quantum state; we also compare this phenomenon to the effectsof thermal noise. Using the rapid dephasing near an instability, we propose amethod for the direct measurement of scattering lengths.Comment: 17 pages, 9 figures, Phys. Rev. A 64, 0136XX (2001

Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theory