| Autor: |
Nakamura, Katsuhiro, Babajanov, Doniyor, Matrasulov, Davron, Kobayashi, Michikazu, Muruganandam, Paulsamy |
| Rok vydání: |
2016 |
| Předmět: |
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| Zdroj: |
J. Phys. A: Math. Theor. 49 (2016) 315102 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1088/1751-8113/49/31/315102 |
| Popis: |
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 2 dimensions under the strong repulsive cubic nonlinearity. As 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 Pad\'e approximation which accommodates a hallmark of the vortex core. We have obtained 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 Gross-Pitaevskii equation. In higher-energy states of 2 vortex systems, the breathing width degree of freedom plays role of a kicking in the kicked rotator and generates chaos with a structure of sea-urchin needles. Byproduct of the present variational approach includes: (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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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