Chaos in a Bose–Einstein condensate

doi:10.1088/1674-1056/19/11/113205

Abstract It is demonstrated that Smale-horseshoe chaos exists in the time evolution of the one-dimensional Bose–Einstein condensate driven by time-periodic harmonic or inverted-harmonic potential. A formally exact solution of the time-dependent Gross–Pitaevskii equation is constructed, which describes the matter shock waves with chaotic or periodic amplitudes and phases.

Keywords: Bose–Einstein condensate chaos Gross–Pitaevskii equation

Received: 03 February 2010
Revised: 04 June 2010
Accepted manuscript online:

PACS:	03.75.Nt	(Other Bose-Einstein condensation phenomena)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China(Grant No. 10871203).

Cite this article:

Wang Zhi-Xia(王志霞), Ni Zheng-Guo(倪政国), Cong Fu-Zhong(从福仲), Liu Xue-Shen(刘学深), and Chen Lei(陈蕾) Chaos in a Bose–Einstein condensate 2010 Chin. Phys. B 19 113205

[1]	Parthasarathy S 1992 Phys. Rev. A 46 2147
[2]	Wang Z X, Zhang X H and Shen K 2008 Chin. Phys. B 17 3270
[3]	Wang Z X, Zhang X H and Shen K 2008 J. Low. Temp. Phys. 152 136
[4]	Wang Z X, Zhang X H and Shen K 2008 J. Exp. Theor. Phys. 5 134
[5]	Wang Z X and Shen K 2008 Cen. Eup. J. Phys. 6 402
[6]	Wang Z X, Zhang X H and Shen K 2008 Acta Phys. Sin. 57 7586
[7]	Wang Z X, Zhang X H and Shen K 2008 Commun. Theor. Phys. 50 215
[8]	Venkatesan A, Lakshmanan M, Prasad A and Ramaswamy R 2000 Phys. Rev. E 61 3641
[9]	Dalfovo F, Giorgini S, Pitaevskii L P and Stringari S 1999 Rev. Mod. Phys. 71 463
[10]	Leggett A J 2001 Rev. Mod. Phys. 73 307
[11]	Matsumoto S and Yoshimura M 2000 Phys. Rev. A 63 012104
[12]	Zurek W H and Paz J P 1994 Phys. Rev. Lett. 72 2508
[13]	Haydock R, Nex C M M and Simons B D 1999 Phys. Rev. E 59 5292
[14]	Khaykovich L, Schreck F, Ferrari G, Bourdel T, Cubizilles J, Carr L D, Castin Y and Salomon C 2002 Science 296 1290
[15]	Liang Z X, Zhang Z D and Liu W M 2005 Phys. Rev. Lett. 94 050402
[16]	Xue J K 2005 J. Phys. B 38 3841
[17]	Castin Y and Dum R 1996 Phys. Rev. Lett. 77 5315
[18]	Abdullaev F K and Galimzyanov R 2003 J. Phys. B 36 1099
[19]	Horng T L, Hsueh C H and Gou S C 2008 Phys. Rev. A 77 063625
[20]	Hoefer M A, Ablowitz M J, Coddington I, Cornell E A, Engels P and Schweikhard V 2006 Phys. Rev. A 74 023623
[21]	Simula T P, Engels P, Coddington I, Schweikhard V, Cornell E A and Ballagh R J 2005 Phys. Rev. Lett. 94 080404
[22]	Abdullaev F K and Galimzyanov R 2003 J. Phys. B 36 1099
[23]	Hoefer M A, Ablowitz M J, Coddington I, Cornell E A, Engels P and Schweikhard V 2006 Phys. Rev. A 74 023623
[24]	Perez-Garcia V M, Konotop V V and Brazhnyi V A 2004 Phys. Rev. Lett. 92 220403
[25]	Hai W, Zhu Q and Rong S 2009 Phys. Rev. A 79 023603
[26]	Wolf A S, Wift J B and Swinney H L 1985 Physica D 16 285
[27]	Pachos J K and Knight P L 2003 Phys. Rev. Lett. 91 107902
[28]	Xu J, Hai W H and Li H 2007 Chin. Phys. 16 2244
[29]	Chen Q, Hai K and Hai W H 2007 Chin. Phys. 16 3662
[30]	Furuya K, Nemes M C and Pellegrino G O 1998 Phys. Rev. Lett. 80 5524
[31]	Song P H and Shepelyansky D L 2001 Phys. Rev. Lett. 86 2162

[1]	An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. Chin. Phys. B, 2023, 32(3): 030203.
[2]	A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain Chunlei Fan(范春雷) and Qun Ding(丁群). Chin. Phys. B, 2023, 32(1): 010501.
[3]	Memristor hyperchaos in a generalized Kolmogorov-type system with extreme multistability Xiaodong Jiao(焦晓东), Mingfeng Yuan(袁明峰), Jin Tao(陶金), Hao Sun(孙昊), Qinglin Sun(孙青林), and Zengqiang Chen(陈增强). Chin. Phys. B, 2023, 32(1): 010507.
[4]	Synchronously scrambled diffuse image encryption method based on a new cosine chaotic map Xiaopeng Yan(闫晓鹏), Xingyuan Wang(王兴元), and Yongjin Xian(咸永锦). Chin. Phys. B, 2022, 31(8): 080504.
[5]	Multi-target ranging using an optical reservoir computing approach in the laterally coupled semiconductor lasers with self-feedback Dong-Zhou Zhong(钟东洲), Zhe Xu(徐喆), Ya-Lan Hu(胡亚兰), Ke-Ke Zhao(赵可可), Jin-Bo Zhang(张金波),Peng Hou(侯鹏), Wan-An Deng(邓万安), and Jiang-Tao Xi(习江涛). Chin. Phys. B, 2022, 31(7): 074205.
[6]	Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network Ai-Xue Qi(齐爱学), Bin-Da Zhu(朱斌达), and Guang-Yi Wang(王光义). Chin. Phys. B, 2022, 31(2): 020502.
[7]	Energy spreading, equipartition, and chaos in lattices with non-central forces Arnold Ngapasare, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Charalampos Skokos. Chin. Phys. B, 2022, 31(2): 020506.
[8]	Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[9]	Resonance and antiresonance characteristics in linearly delayed Maryland model Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Chin. Phys. B, 2022, 31(12): 120502.
[10]	An image encryption algorithm based on spatiotemporal chaos and middle order traversal of a binary tree Yining Su(苏怡宁), Xingyuan Wang(王兴元), and Shujuan Lin(林淑娟). Chin. Phys. B, 2022, 31(11): 110503.
[11]	Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system Yue Li(李月), Zengqiang Chen(陈增强), Zenghui Wang(王增会), and Shijian Cang(仓诗建). Chin. Phys. B, 2022, 31(1): 010501.
[12]	Dynamics analysis in a tumor-immune system with chemotherapy Hai-Ying Liu(刘海英), Hong-Li Yang(杨红丽), and Lian-Gui Yang(杨联贵). Chin. Phys. B, 2021, 30(5): 058201.
[13]	Control of chaos in Frenkel-Kontorova model using reinforcement learning You-Ming Lei(雷佑铭) and Yan-Yan Han(韩彦彦). Chin. Phys. B, 2021, 30(5): 050503.
[14]	Resistance fluctuations in superconducting K_xFe_2-ySe₂ single crystals studied by low-frequency noise spectroscopy Hai Zi(子海), Yuan Yao(姚湲), Ming-Chong He(何明冲), Di Ke(可迪), Hong-Xing Zhan(詹红星), Yu-Qing Zhao(赵宇清), Hai-Hu Wen(闻海虎), and Cong Ren(任聪). Chin. Phys. B, 2021, 30(4): 047402.
[15]	A multi-directional controllable multi-scroll conservative chaos generator: Modelling, analysis, and FPGA implementation En-Zeng Dong(董恩增), Rong-Hao Li(李荣昊), and Sheng-Zhi Du(杜升之). Chin. Phys. B, 2021, 30(2): 020505.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Chaos in a Bose–Einstein condensate

Cite this article:

Online attention