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研究了Born-Oppenheimer近似下谐振子场驱动电磁模系统的Berry相和Hannay角, 通过理论计算得到了其表达式, 并讨论了这二者之间的半经典关系.结果表明, 这一量子Born-Oppenheimer复合系统的Berry相包含两部分: 第一部分与通常几何相的定义相同, 另一项则是由耦合造成的有效规范式引入的.这一量子修正可以被看作一个等效的Aharonov-Bohm效应.不仅如此, 其对应经典系统的Hannay角的定义中也存在类似的现象. 由此可见, 这一复合系统的Berry相与Hannay角之间也存在半经典关系, 并与文献[16] 中通常情况下的半经典关系相同.此外, 上述理论也可以运用于解决产生中性原子的人造规范势等物理问题.
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关键词:
- Berry相 /
- Hannay角 /
- 量子经典对应 /
- Born-Oppenheimer近似
In this paper, we investigate the Berry phase and Hannay's angle of an electromagnetic mode system driven by harmonic field with Born-Oppenheimer approximation and obtain their algebraic expressions by theoretical calculation. The semiclassical relation between Berry phase and Hannay's angle is discussed. We find that besides the usual connection term, the Berry phase of BO hybrid system contains a novel term brought forth by the coupling induced effective gauge potential. This quantum modification can be viewed as an effective Aharonov-Bohm effect. Moreover, a similar phenomenon is founded in the Hannay's angle of classical BO hybrid system, which indicates that the Berry phase and Hannay's angle possess the same relation as the usual one. Besides, our theory can also be used to generate Artificial gauge potentials for neutral atoms.-
Keywords:
- Berry phase /
- Hannay's angle /
- quantum-classical correspondence /
- Born-Oppenheimer approximation
[1] Born M, Oppenheimer J 1927 Ann. Phys. 84 457
[2] Berry M V 1984 Proc. R. Soc. A 392 45
[3] Chruściński D, Jamiolkowski A 2004 Geometric Phases in Classical and Quantum Mechanics (Berlin: Birkhäuser)
[4] Berry M V 1990 edited by Bregda U, Garmo G, Morandi G Anomalies, Phases, Defects (Naples: Bibliopolis)
[5] Robbins J M 1997 arXiv1008.5331.
[6] Bohm A, Mostafazadeh A, Koizumi H, Niu N, Zwanziger J 2003 The Geometric Phase in Quantum Systems (Berlin: Springe-Verlag)
[7] Xiao D, Zhang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
[8] Wang L C, Yan J Y, Yi X X 2010 Chin. Phys. B 19 040512
[9] Jia X Y, Li W D, Liang J Q 2007 Chin. Phys. 16 2855
[10] Wu J W, Guo G C 1995 Chin. Phys. 4 406
[11] Liu H D, Yi X X 2011 Phys. Rev. A 84 022114
[12] Shan C J 2012 Acta Phys. Sin. 61 220302 (in Chinese) [单传家 2012 61 220302]
[13] Simon B 1983 Phys. Rev. Lett. 51 2167
[14] Arnold V I 1978 Mathematical Methods of Classical Mechanics (Berlin: Springer-Verlag)
[15] Hannay J H 1985 J. Phys. A 18 221
[16] Berry M V 1985 J. Phys. A 18 15
[17] Giavarini G, Gozzi E, Rohrlich D, Thacker W D 1989 Phys. Rev. D 39 3007
[18] Jarzynski C 1995 Phys. Rev. Lett. 74 1264
[19] Pati A K 1998 Ann. Phys. 270 178
[20] Liu J, Hu B, Li B W 1998 Phys. Rev. Lett. 81 1749
[21] Fu L B, Liu J 2010 Ann. Phys. 325 2425
[22] Mead C A, Truhlar D 1979 J. Chem. Phys. 70 2284
[23] Mead C A 1992 Rev. Mod. Phys. 64 51
[24] Stone M 1986 Phys. Rev. D 33 1191
[25] Berry M V, Robbins J M 1993 Proc. R. Soc. A 442 659
[26] Gozzi E, Thacker W D 1987 Phys. Rev. D 35 2398
[27] Sun C P, Ge M L 1990 Phys. Rev. D 41 1349
[28] Zhang Q, Wu B 2006 Phys. Rev. Lett. 97 190401
[29] Liu H D, Wu S L, Yi X X 2011 Phys. Rev. A 83 062101
[30] Aharonov Y, Bohm D 1959 Phys. Rev. 115 485
[31] Dalibard J, Gerbier F, Juzeliunas G, Öhberg P 2011 Rev. Mod. Phys. 83 1523
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[1] Born M, Oppenheimer J 1927 Ann. Phys. 84 457
[2] Berry M V 1984 Proc. R. Soc. A 392 45
[3] Chruściński D, Jamiolkowski A 2004 Geometric Phases in Classical and Quantum Mechanics (Berlin: Birkhäuser)
[4] Berry M V 1990 edited by Bregda U, Garmo G, Morandi G Anomalies, Phases, Defects (Naples: Bibliopolis)
[5] Robbins J M 1997 arXiv1008.5331.
[6] Bohm A, Mostafazadeh A, Koizumi H, Niu N, Zwanziger J 2003 The Geometric Phase in Quantum Systems (Berlin: Springe-Verlag)
[7] Xiao D, Zhang M C, Niu Q 2010 Rev. Mod. Phys. 82 1959
[8] Wang L C, Yan J Y, Yi X X 2010 Chin. Phys. B 19 040512
[9] Jia X Y, Li W D, Liang J Q 2007 Chin. Phys. 16 2855
[10] Wu J W, Guo G C 1995 Chin. Phys. 4 406
[11] Liu H D, Yi X X 2011 Phys. Rev. A 84 022114
[12] Shan C J 2012 Acta Phys. Sin. 61 220302 (in Chinese) [单传家 2012 61 220302]
[13] Simon B 1983 Phys. Rev. Lett. 51 2167
[14] Arnold V I 1978 Mathematical Methods of Classical Mechanics (Berlin: Springer-Verlag)
[15] Hannay J H 1985 J. Phys. A 18 221
[16] Berry M V 1985 J. Phys. A 18 15
[17] Giavarini G, Gozzi E, Rohrlich D, Thacker W D 1989 Phys. Rev. D 39 3007
[18] Jarzynski C 1995 Phys. Rev. Lett. 74 1264
[19] Pati A K 1998 Ann. Phys. 270 178
[20] Liu J, Hu B, Li B W 1998 Phys. Rev. Lett. 81 1749
[21] Fu L B, Liu J 2010 Ann. Phys. 325 2425
[22] Mead C A, Truhlar D 1979 J. Chem. Phys. 70 2284
[23] Mead C A 1992 Rev. Mod. Phys. 64 51
[24] Stone M 1986 Phys. Rev. D 33 1191
[25] Berry M V, Robbins J M 1993 Proc. R. Soc. A 442 659
[26] Gozzi E, Thacker W D 1987 Phys. Rev. D 35 2398
[27] Sun C P, Ge M L 1990 Phys. Rev. D 41 1349
[28] Zhang Q, Wu B 2006 Phys. Rev. Lett. 97 190401
[29] Liu H D, Wu S L, Yi X X 2011 Phys. Rev. A 83 062101
[30] Aharonov Y, Bohm D 1959 Phys. Rev. 115 485
[31] Dalibard J, Gerbier F, Juzeliunas G, Öhberg P 2011 Rev. Mod. Phys. 83 1523
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