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

Hisatsugu Yamasaki·Yuhei Natsume·Katsuhiro Nakamura
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Abstract

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{ö}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.

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Hisatsugu Yamasaki, Yuhei Natsume, Katsuhiro Nakamura. 2005-05-21. A model for conservative chaos constructed from multi-component Bose-Einstein condensates with a trap in 2 dimensions. https://doi.org/10.1143/jpsj.74.1887

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