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Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential |
| Fang Jian-Shu(方见树)a)b)† and Liao Xiang-Ping(廖湘萍)a) |
| a Institute of Physics, Hunan University of Technology, Zhuzhou 412008, China; b College of Science, Hunan University of Technology, Zhuzhou 412008, China |
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Abstract Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose-Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.
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Received: 22 October 2010
Revised: 15 November 2010
Accepted manuscript online:
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PACS:
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03.75.Lm
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(Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations)
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05.45.Ac
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(Low-dimensional chaos)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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| Fund: Project supported by the Natural Science Foundation of Hunan Province of China (Grant No. 10JJ3088) and the Key Research Foundation of the Education Bureau of Hunan Province of China (Grant Nos. 08A015 and 10A026). |
Cite this article:
Fang Jian-Shu(方见树) and Liao Xiang-Ping(廖湘萍) Stability of trapped Bose–Einstein condensates in one-dimensional tilted optical lattice potential 2011 Chin. Phys. B 20 040310
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