Chaotic Oscillations in Finite Quantum Systems: Trapped Bose-Einstein Condensates

We discuss the recently achieved Bose-Einstein condensation for alkali-metal atoms in magnetic traps. The theoretically predicted low-energy collective oscillations of the condensate have been experimentally confirmed by laser imaging techniques. We show by using Poincar`e sections that at higher energies non-linear effects appear and oscillations become chaotic. PACS 03.75.Fi, 05.30.Jp, 05.45.+b, 32.80.Pj