Fate of a Bose-Einstein condensate with an attractive interaction

We calculate the decay amplitude of a harmonically trapped Bose-Einstein condensate with attractive interaction via the Feynman path integral. We find that when the number of particles is less than a critical number, the condensate decays relatively slowly through quantum tunneling. When the number exceeds a critical one, a “black hole” opens up at the center of the trap, in which density fluctuations become large due to a negative pressure, and inelastic collisions will drain the particles from the trap. As the black hole is fed by tunneling particles, we have a novel system in which quantum tunneling serves as a hydrodynamic source.