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In this paper, we study the spatially chaotic distribution of atoms in a Bose-Einstein condensate system, trapped in an asymmetric periodic potential. For a constant phase of condensate, without atom currents in the system, the space distributed structure of condensated atoms can be described by an undamped Duffing equation with double drivers. Through theoretical analyses, the Mel'nikov chaotic criterion for the system with a repulsive interatomic interaction is presented. Numerical simulations show that an increasing chemical potential can exert considerable suppression on the chaotic distribution of condensated atoms and even completely eliminate chaos. For a system with an attractive interatomic interaction, under some specific parametric conditions, adjusting the ratio between optical lattice potential amplitudes will force the condensated atoms from a periodic state into a spatially chaotic distribution; with the increase of chemical potential, the spatially chaotic distribution is completely suppressed.
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Keywords:
- Bose-Einstein condensates /
- Mel'nikov function /
- chaos
[1] Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463
[2] Zhou S Y, Long Q, Zhou S Y, Fu H X, Wang Y Z 2002 Physics 31 481(in Chinese)[周蜀渝、龙 全、周善钰、付海翔、王育竹 2002 物理 31 481]
[3] Smerzi A, Fantoni S, Giovanazzi S, Shenoy S R 1997 Phys. Rev. Lett. 79 4950
[4] Raghavan S, Smerzi A, Fantoni S, Shenoy S R 1999 Phys. Rev. A 59 620
[5] Milburm G J, Corney J, Wright E M, Walls D F 1997 Phys. Rev. A 55 4318
[6] Wu B, Niu Q 2000 Phys. Rev. A 61 023402
[7] Liu W M, Wu B, Niu Q 2000 Phys. Rev. Lett. 84 2294
[8] Xue J K 2005 J. Phys. B 38 3841
[9] Filho V S, Gammal A, Frederico T, Tomio L 2000 Phys. Rev. A 62 033605
[10] Abdullaev F K, Kraenkel R A 2000 Phys. Rev. A 62 023613
[11] Hai W, Lee C, Chong G, Shi L 2002 Phys. Rev. E 66 026202
[12] Liu J, Zhang C, Raizen M, Niu Q 2006 Phys. Rev. A 73 013601
[13] Hai W, Zhu Q, Rong S 2009 Phys. Rev. A 79 023603
[14] Hai W, Rong S, Zhu Q 2008 Phys. Rev. E 78 066214
[15] Chong G, Hai W, Xie Q 2005 Phys. Rev. E 71 016202
[16] Chong G, Hai W, Xie Q 2004 Chaos 14 217
[17] Xu J, Hai W, Li H 2007 Chin. Phys. 16 2244
[18] Xie Q, Rong S, Zhong H, Lu G, Hai W 2010 Phys. Rev. A 82 023616
[19] Li F, Shu W, Luo H, Ren Z 2007 Chin. Phys. 16 650
[20] Li F, Shu W, Jiang J, Luo H, Ren Z 2007 Eur. Phys. J. D 41 355
[21] Li F, Ren Z, Luo H, Shu W, Wu Q 2007 Commun. Theor. Phys. 48 107
[22] Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 (in Chinese) [王冠芳、傅立斌、赵 鸿、刘 杰 2005 54 5003]
[23] Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 661 (in Chinese)[房永翠、杨志安、杨丽云 2008 57 661]
[24] Chen H J, Xue J K 2008 Acta Phys. Sin. 57 3962 (in Chinese)[陈海军、薛具奎 2008 57 3962]
[25] Wang G F, Liu H 2008 Acta Phys. Sin. 57 667 (in Chinese) [王冠芳、刘 红 2008 57 667]
[26] Xi Y D, Wang D L, She Y C, Wang F J, Ding J W 2010 Acta Phys.Sin. 59 3720 (in Chinese)[奚玉东、王登龙、佘彦超、王凤姣、丁建文 2010 59 3720]
[27] Li F, Zhou B, Shu W, Luo H, Huang Z, Tian L 2008 Eur. Phys. J. D 50 75
[28] Long Y J 1996 Chaotic Vibration Research: Approach and Practice (Beijing: Tsinghua University Press) p39 (in Chinese) [龙运佳 1996 混沌振动研究:方法与实践 (北京:清华大学出版社) 第39页]
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[1] Dalfovo F, Giorgini S, Pitaevskii L P, Stringari S 1999 Rev. Mod. Phys. 71 463
[2] Zhou S Y, Long Q, Zhou S Y, Fu H X, Wang Y Z 2002 Physics 31 481(in Chinese)[周蜀渝、龙 全、周善钰、付海翔、王育竹 2002 物理 31 481]
[3] Smerzi A, Fantoni S, Giovanazzi S, Shenoy S R 1997 Phys. Rev. Lett. 79 4950
[4] Raghavan S, Smerzi A, Fantoni S, Shenoy S R 1999 Phys. Rev. A 59 620
[5] Milburm G J, Corney J, Wright E M, Walls D F 1997 Phys. Rev. A 55 4318
[6] Wu B, Niu Q 2000 Phys. Rev. A 61 023402
[7] Liu W M, Wu B, Niu Q 2000 Phys. Rev. Lett. 84 2294
[8] Xue J K 2005 J. Phys. B 38 3841
[9] Filho V S, Gammal A, Frederico T, Tomio L 2000 Phys. Rev. A 62 033605
[10] Abdullaev F K, Kraenkel R A 2000 Phys. Rev. A 62 023613
[11] Hai W, Lee C, Chong G, Shi L 2002 Phys. Rev. E 66 026202
[12] Liu J, Zhang C, Raizen M, Niu Q 2006 Phys. Rev. A 73 013601
[13] Hai W, Zhu Q, Rong S 2009 Phys. Rev. A 79 023603
[14] Hai W, Rong S, Zhu Q 2008 Phys. Rev. E 78 066214
[15] Chong G, Hai W, Xie Q 2005 Phys. Rev. E 71 016202
[16] Chong G, Hai W, Xie Q 2004 Chaos 14 217
[17] Xu J, Hai W, Li H 2007 Chin. Phys. 16 2244
[18] Xie Q, Rong S, Zhong H, Lu G, Hai W 2010 Phys. Rev. A 82 023616
[19] Li F, Shu W, Luo H, Ren Z 2007 Chin. Phys. 16 650
[20] Li F, Shu W, Jiang J, Luo H, Ren Z 2007 Eur. Phys. J. D 41 355
[21] Li F, Ren Z, Luo H, Shu W, Wu Q 2007 Commun. Theor. Phys. 48 107
[22] Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 (in Chinese) [王冠芳、傅立斌、赵 鸿、刘 杰 2005 54 5003]
[23] Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 661 (in Chinese)[房永翠、杨志安、杨丽云 2008 57 661]
[24] Chen H J, Xue J K 2008 Acta Phys. Sin. 57 3962 (in Chinese)[陈海军、薛具奎 2008 57 3962]
[25] Wang G F, Liu H 2008 Acta Phys. Sin. 57 667 (in Chinese) [王冠芳、刘 红 2008 57 667]
[26] Xi Y D, Wang D L, She Y C, Wang F J, Ding J W 2010 Acta Phys.Sin. 59 3720 (in Chinese)[奚玉东、王登龙、佘彦超、王凤姣、丁建文 2010 59 3720]
[27] Li F, Zhou B, Shu W, Luo H, Huang Z, Tian L 2008 Eur. Phys. J. D 50 75
[28] Long Y J 1996 Chaotic Vibration Research: Approach and Practice (Beijing: Tsinghua University Press) p39 (in Chinese) [龙运佳 1996 混沌振动研究:方法与实践 (北京:清华大学出版社) 第39页]
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