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In this paper, we have investigated the off-diagonal Berry phase of nonlinear systems and presented its explicit expression. The results show that, for nonlinear systems, the off-diagonal berry phase contains a new term in addition to the dynamical phase, the geometric phase and the nonlinear phase. This new term can describe a cross effect between the Bogoliubov excitation around one eigenstate and another instantaneous eigenstate, while the Bogoliubov excitations are found to be accumulated during the adiabatic evolution and contribute a finite phase of geometric nature. As an application, the off-diagonal Berry phase of a two-well trapped Bose-Einstein condensate system is calculated.
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Keywords:
- Berry phase /
- off-diagonal /
- adiabatic evolution /
- Bose-Einstein condensates
[1] Smerzi A, Fantoni S, Giovanazzi S, Shenoy S R 1997 Phys. Rev. Lett. 79 4950
[2] Milburn G J, Corney J 1997 Phys. Rev. A 55 4318
[3] Mewes M O, Andrews M R, Kurn D M, Durfee D S, Townsend C G, Ketterle W 1997 Phys. Rev. Lett. 78 582
[4] Dalfovo F, Giorgini S, PitaevskiiL P 1999 Rev. Mod. Phys. 71 463
[5] Liu J, Fu L B, Ou B Y, Chen S G, Choi D I, Wu B, Niu Q 2002 Phys. Rev. A 66 023404
[6] Wang S, Yang Z A 2009 Acta Phys. Sin. 58 3699 (in Chinese) [王沙, 杨志安 2009 58 3699]
[7] Feldmann J, Leo K, Shah J, Miller D A B 1992 Phys. Rev. B 46 7252
[8] Berry M V 1984 Proc. R. Soc. London A 45 392
[9] Simon B 1983 Phys. Rev. Lett. 51 2167
[10] Li H Z 1998 Global Properties Simple Physical Systems (Shanghai: Shanghai Scientific & Technical Publishers) (in Chinese) [李华钟 1998 简单物理的整体性贝里相位及其他 (上海: 上海科技出版社)]
[11] Bohm A, Mostafazadeh A, Koizumi H 2003 The GeometricPhase in Quantum Systems (New York: Sp ringer)
[12] Manini N, Pistolesi F, 2000 Phys. Rev. Lett. 85 3067
[13] Liu J, Wu B, Niu Q 2003 Phys. Rev. Lett. 90 170404
[14] Wu B, Liu J, Niu Q 2005 Phys. Rev. Lett. 94 140402
[15] Liu J, Fu L B, 2010 Phys. Rev. A 81 052112
[16] Li S C, Liu J, Fu L B 2011 Phys. Rev. A 83 042107
[17] Li S C, Fu L B, Liu J 2011 Phys. Rev. A 84 053610
[18] Pethick C J, Smith H 2002 Bose-Einstein Condensation in Dilute Gases (London: Cambridge University Press)
[19] 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 2009 57 661]
[20] 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]
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[1] Smerzi A, Fantoni S, Giovanazzi S, Shenoy S R 1997 Phys. Rev. Lett. 79 4950
[2] Milburn G J, Corney J 1997 Phys. Rev. A 55 4318
[3] Mewes M O, Andrews M R, Kurn D M, Durfee D S, Townsend C G, Ketterle W 1997 Phys. Rev. Lett. 78 582
[4] Dalfovo F, Giorgini S, PitaevskiiL P 1999 Rev. Mod. Phys. 71 463
[5] Liu J, Fu L B, Ou B Y, Chen S G, Choi D I, Wu B, Niu Q 2002 Phys. Rev. A 66 023404
[6] Wang S, Yang Z A 2009 Acta Phys. Sin. 58 3699 (in Chinese) [王沙, 杨志安 2009 58 3699]
[7] Feldmann J, Leo K, Shah J, Miller D A B 1992 Phys. Rev. B 46 7252
[8] Berry M V 1984 Proc. R. Soc. London A 45 392
[9] Simon B 1983 Phys. Rev. Lett. 51 2167
[10] Li H Z 1998 Global Properties Simple Physical Systems (Shanghai: Shanghai Scientific & Technical Publishers) (in Chinese) [李华钟 1998 简单物理的整体性贝里相位及其他 (上海: 上海科技出版社)]
[11] Bohm A, Mostafazadeh A, Koizumi H 2003 The GeometricPhase in Quantum Systems (New York: Sp ringer)
[12] Manini N, Pistolesi F, 2000 Phys. Rev. Lett. 85 3067
[13] Liu J, Wu B, Niu Q 2003 Phys. Rev. Lett. 90 170404
[14] Wu B, Liu J, Niu Q 2005 Phys. Rev. Lett. 94 140402
[15] Liu J, Fu L B, 2010 Phys. Rev. A 81 052112
[16] Li S C, Liu J, Fu L B 2011 Phys. Rev. A 83 042107
[17] Li S C, Fu L B, Liu J 2011 Phys. Rev. A 84 053610
[18] Pethick C J, Smith H 2002 Bose-Einstein Condensation in Dilute Gases (London: Cambridge University Press)
[19] 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 2009 57 661]
[20] 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]
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