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物性研究

Transition to chaos in Bose-Einstein condensates: role of inter-component interactions on wavepacket breathing (量子系およびマクロ系におけるカオスと非線形動力学)

Katsuhiro Nakamura

Published Jun 20, 2005• 0 citations
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Related papers

Transition to chaos in Bose-Einstein condensates : role of inter-component interactions on wavepacket breathing(3) Chaos and nonlinear dynamics in dissipative systems(including BEC and pattern formations), Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)

Katsuhiro Nakamura

この論文は国立情報学研究所の電子図書館事業により電子化されました。

物性研究•Jun 20, 2005•0 citations

Formation of multiple domains and quantized vortices in two-component Bose-Einstein condensates (量子系およびマクロ系におけるカオスと非線形動力学)

Kenichi Kasamatsu

物性研究•Jun 20, 2005•0 citations

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

Hisatsugu Yamasaki, Yuhei Natsume, Katsuhiro Nakamura

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.

arXiv:cond-mat/0505527•Journal of the Physical Society of Japan•Jul 1, 2005•3 citations

Dynamical and Wave Chaos in the Bose–Einstein Condensate

William P. Reinhardt, Sarah B. McKinney

Quantum Chaos Y2K•Oct 1, 2001•0 citations

Dynamics of trapped interacting vortices in Bose–Einstein condensates: a role of breathing degree of freedom

Katsuhiro Nakamura, Doniyor Babajanov, Davron Matrasulov +2 more

Abstract With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose–Einstein condensates in two dimensions, under strong repulsive cubic nonlinearity. For the trial function, we choose a product of two vortex functions, assuming a pair interaction, and employ the amplitude form of each vortex function in the Padé approximation, which accommodates a hallmark of the vortex core. We obtain the Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivative of width and also its Hamilton formalism by having recourse to a non-standard Poisson bracket. By solving the Hamilton equation, we find rapid radial breathing oscillations superposed on the slower rotational motion of vortex cores, consistent with numerical solutions of the Gross–Pitaevskii equation. In higher-energy states of two vortex systems, the breathing width degree of freedom plays the role of a kicking in the kicked rotator, and generates chaos with a structure of sea-urchin needles. The by-products of the present variational approach include: (1) the charge-dependent logarithmic inter-vortex interaction multiplied with a pre-factor, which depends on the scalar product of a pair of core-position vectors; (2) the charge-independent short-range repulsive inter-vortex interaction and spring force.

arXiv:1607.00201•Journal of Physics A Mathematical and Theoretical•Jun 30, 2016•6 citations

Chaotic Dynamics for the Two-component Bose-Einstein Condensate System

Jibin Li

Interdisciplinary mathematical sciences•Jan 1, 2010•0 citations
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-ddd 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.
Abstract With use of a variational principle, we investigate a role of breathing width degree of freedom in the effective theory of interacting vortices in a trapped single-component Bose–Einstein condensates in two dimensions, under strong repulsive cubic nonlinearity. For the trial function, we choose a product of two vortex functions, assuming a pair interaction, and employ the amplitude form of each vortex function in the Padé approximation, which accommodates a hallmark of the vortex core. We obtain the Lagrange equation for the interacting vortex-core coordinates coupled with the time-derivative of width and also its Hamilton formalism by having recourse to a non-standard Poisson bracket. By solving the Hamilton equation, we find rapid radial breathing oscillations superposed on the slower rotational motion of vortex cores, consistent with numerical solutions of the Gross–Pitaevskii equation. In higher-energy states of two vortex systems, the breathing width degree of freedom plays the role of a kicking in the kicked rotator, and generates chaos with a structure of sea-urchin needles. The by-products of the present variational approach include: (1) the charge-dependent logarithmic inter-vortex interaction multiplied with a pre-factor, which depends on the scalar product of a pair of core-position vectors; (2) the charge-independent short-range repulsive inter-vortex interaction and spring force.