A Model for Conservative Chaos Constructed from Multicomponent Bose–Einstein Condensates with a Trap in Two Dimensions

Abstract

To elucidate the mechanism leading to the breakdown of a particle picture for multicomponent Bose–Einstein condensates (BECs) with a harmonic trap in high dimensions, we investigate the corresponding two-dimensional nonlinear Schrödinger equation (Gross–Pitaevskii equation) using a modified variational principle. A molecule of two identical Gaussian wave packets has two degrees of freedom (DFs): the separation of center of masses and the wave-packet width. Without intercomponent interaction (ICI), these DFs show independent regular oscillations with degenerate eigenfrequencies. The inclusion of ICI strongly mixes these DFs, generating a fat mode that breaks the particle picture, which, however, can be recovered by introducing a time-periodic ICI with zero average. In the case of a molecule of three wave packets for a three-component BEC, the increase of the ICI amplitude yields a transition from regular to chaotic oscillations in wave-packet breathing.