A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions

To show a mechanism leading to the breakdown of a particle picture for the multi-component Bose-Einstein condensates(BECs) with a harmonic trap in high dimensions, we investigate the corresponding 2-$d$ nonlinear Schr{\"o}dinger equation (Gross-Pitaevskii equation) with use of a modified variational principle. A molecule of two identical Gaussian wavepackets has two degrees of freedom(DFs), the separation of center-of-masses and the wavepacket width. Without the inter-component interaction(ICI) these DFs show independent regular oscillations with the degenerate eigen-frequencies. The inclusion of ICI strongly mixes these DFs, generating a fat mode that breaks a particle picture, which however can be recovered by introducing a time-periodic ICI with zero average. In case of the molecule of three wavepackets for a three-component BEC, the increase of amplitude of ICI yields a transition from regular to chaotic oscillations in the wavepacket breathing.