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Dynamics of vibrational chaos and entanglement in triatomic molecules: Lie algebraic model |
Zhai Liang-Jun(翟良君), Zheng Yu-Jun(郑雨军)†, and Ding Shi-Liang(丁世良) |
School of Physics, Shandong University, Jinan 250100, China |
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Abstract In this paper, the dynamics of chaos and the entanglement in triatomic molecular vibrations are investigated. On the classical aspect, we study the chaotic trajectories in the phase space. We employ the linear entropy to examine the dynamical entanglement of the two bonds on the quantum aspect. The correspondence between the classical chaos and the quantum dynamical entanglement is also investigated. As an example, we apply our algebraic model to molecule H2O.
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Received: 07 January 2012
Revised: 20 February 2012
Accepted manuscript online:
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PACS:
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05.45.Ac
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(Low-dimensional chaos)
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05.45.Mt
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(Quantum chaos; semiclassical methods)
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33.20.Tp
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(Vibrational analysis)
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03.67.Mn
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(Entanglement measures, witnesses, and other characterizations)
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Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 91021009 and 10874102) and the National Basic Research Program of China (Grant No. 2009CB929404). |
Corresponding Authors:
Zheng Yu-Jun
E-mail: yzheng@sdu.edu.cn
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Cite this article:
Zhai Liang-Jun(翟良君), Zheng Yu-Jun(郑雨军), and Ding Shi-Liang(丁世良) Dynamics of vibrational chaos and entanglement in triatomic molecules: Lie algebraic model 2012 Chin. Phys. B 21 070503
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[1] |
Fujisaki H, Miyadera T and Tanaka A 2003 Phys. Rev. E 67 066201
|
[2] |
Gu S, Deng S, Li Y and Lin H 2004 Phys. Rev. Lett. 93 086402
|
[3] |
Yu T and Eberly J H 2009 Science 323 598
|
[4] |
Hou X W, Chen J H and Ma Z Q 2006 Phys. Rev. A 74 062513
|
[5] |
Liu Y, Zheng Y J, Ren W Y and Ding S L 2008 Phys. Rev. A 78 032523
|
[6] |
Milman P and Keller A 2009 Phys. Rev. A 79 052303
|
[7] |
Cai J M, Popescu S and Briegel H J 2010 Phys. Rev. E 82 021921
|
[8] |
Tesch C M and de Vivie-Riedle R 2002 Phys. Rev. Lett. 89 157901
|
[9] |
Zhao M Y and Babikov D 2006 J. Chem. Phys. 125 024105
|
[10] |
Diaz A and Jung C 2008 Mol. Phys. 106 787
|
[11] |
Huang J and Wu G Z 2007 Chem. Phys. Lett. 439 231
|
[12] |
Sako T, Yamanouchi K and Iachello F 2002 J. Chem. Phys. 117 1641
|
[13] |
Ezra G S 1998 Adv. Class. Traj. Meth. 3 35
|
[14] |
Kellman M E and Tyang V 2007 Acc. Chem. Res. 40 243
|
[15] |
Manikandan P, Semparithi A and Keshavamurthy S 2009 J. Phys. Chem. A 113 1717
|
[16] |
Jaff? C and Brumer P 1980 J. Chem. Phys. 73 5646
|
[17] |
Lu Z M and Kellman M E 1997 J. Chem. Phys. 107 6086
|
[18] |
Jung C, Ziemniak E, Carvajal M, Frank A and Lemus R 2001 Chaos 11 464
|
[19] |
Farantos S C 2004 J. Chem. Phys. 126 175101
|
[20] |
Keshavamurthy S and Ezra G S 1997 J. Chem. Phys. 107 156
|
[21] |
Sako T and Yamanouchi K 2001 J. Chem. Phys. 114 9441
|
[22] |
Arranz F J, Seidel L, Giralda C G, Benito R M and Borondo F 2010 Phys. Rev. E 82 026201
|
[23] |
Davis M J 1985 J. Chem. Phys. 83 1016
|
[24] |
Tennyson T and Farantos S C 1985 Chem. Phys. 93 237
|
[25] |
Yu J and Wu G Z 2001 Chem. Phys. Lett. 343 375
|
[26] |
Safi Z S, Losada J C, Benito R M and Borondo F 2008 J. Chem. Phys. 129 164316
|
[27] |
Battisti A, Laplopa R G and Tenenbaum A 2009 Phys. Rev. E 79 046206
|
[28] |
Keshavamurthy S 2007 Int. Rev. Phys. Chem. 26 4
|
[29] |
Carter D and Brumer P 2007 J. Chem. Phys. 126 124307
|
[30] |
Sako T, Yamanouchi K and Iachello F 2000 J. Chem. Phys. 113 7292
|
[31] |
Yang S B and Kellman M E 2000 Phys. Rev. A 62 022105
|
[32] |
Wang X G, Ghose S, Sanders B C and Hu B 2004 Phys. Rev. E 70 0162176
|
[33] |
Ghose S and Sanders B C 2004 Phys. Rev. A 70 062315
|
[34] |
Chaudhury S, Smith A, Anderson B E, Ghose S and Jessen P 2009 Nature 461 768
|
[35] |
Zhang S H and Jie Q L 2008 Phys. Rev. A 77 012312
|
[36] |
SibertIII E L, Reinhardt W P and Hynes J T 1982 J. Chem. Phys. 77 3583
|
[37] |
Hutchinson J S, SibertIII E L and Hynes J T 1984 J. Chem. Phys. 81 1314
|
[38] |
Zheng Y J and Ding S L 2001 Phys. Rev. A 64 032720
|
[39] |
Ding S L and Zheng Y J 1999 J. Chem. Phys. 111 4466
|
[40] |
Zheng Y J and Ding S L 2000 J. Mol. Spectrosco. 201 109
|
[41] |
Zheng Y J and Ding S L 1999 Phys. Lett. A 256 197
|
[42] |
Iachello F and Levine R D 1982 J. Chem. Phys. 77 3046
|
[43] |
Iachello F and Oss S 1991 Phys. Rev. Lett. 66 2976
|
[44] |
Frank A, Lemus R, Bijke R, P閞ez-Bernal F and Arias J M 1996 Ann. Phys. 252 211
|
[45] |
Iachello F and Truini P 1999 Ann. Phys. 276 120
|
[46] |
Feng H R, Liu Y, Zheng Y J, Ren W Y and Ding S L 2007 Phys. Rev. A 75 063417
|
[47] |
Zheng Y 2010 Laser Pulse Phenomena and Applications (New York: INTECH)
|
[48] |
Gilmore R 1981 Catastrophe Theory for Scientists and Engineers (New York: Dover Publications)
|
[49] |
Zheng Y J and Ding S L 1999 Chem. Phys. 247 225
|
[50] |
Zheng Y J and Ding S L 2000 J. Math. Chem. 28 193
|
[51] |
Zheng Y J and Ding S L 2008 Int. J. Quantum. Chem. 108 1059
|
[52] |
Zheng Y J and Ding S L 2000 Chem. Phys. 255 217
|
[53] |
Wilson E B Jr, Decius J C and Cross P C 1955 Molecular Vibrations (New York: Van Nostrand)
|
[54] |
Zaslavsky G M 2007 The Physics of Chaos in Hamiltonian Systems (London: Imperical College Press)
|
[55] |
Chirikov B V 1979 Phys. Rep. 52 263
|
[56] |
Wang X Y and Ding S L 2004 Chem. Phys. 297 111
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