Quantum effects on dynamics of instabilities in Bose-Einstein condensates

Dynamics of fluctuations in unstable Bose-Einstein condensates is analyzed by the solution of approximate operator equations. In the case of a condensate with a negative scattering length the present treatment describes a delay of collapse, in agreement with recent experiments. In the case of a collision of two condensate wavepackets it is shown that quantum effects lead to a Bose enhancement of elastic-scattering losses. In both cases the noncondensate atoms are formed as entangled pairs in squeezed states.