Dynamical entanglement of vibrations in small molecules through an analytically algebraic approach

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 3, 2008, Pages

  Liu, Yan ^a,b   Zheng, Yujun ^a   Ren, Weiyi ^b   Ding, Shiliang ^a  

^a SHANDONG UNIVERSITY   (China)

^b CHINA WEST NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; LATTICE VIBRATIONS; LYAPUNOV FUNCTIONS; MATRIX ALGEBRA; MOLECULES; VIBRATIONS (MECHANICAL);

ALGEBRAIC APPROACHES; ALGEBRAIC MODELING; COHERENT STATES; FOCK STATES; LINEAR ENTROPY; LYAPUNOV; SMALL MOLECULES; VON NEUMANN ENTROPY;

ENTROPY;

EID: 53349160870     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.032523     Document Type: Article

References (56)

1. S. Loyd, Science SCIEAS 0036-8075 261, 1589 (1993).
2. S. J. Gu, S. S. Deng, Y. Q. Li, and H. Q. Lin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.086402 93, 086402 (2004).
3. C. H. Bennett and S. J. Wiesner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2881 69, 2881 (1992).
4. S. Hill and W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.5022 78, 5022 (1997).
5. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1895 70, 1895 (1993).
6. R. Cleve, D. Gottesman, and H. Lo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.83.648 83, 648 (1999).
7. X. W. Hou, M. F. Wan, and Z. Q. Ma, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/j.cplett.2006.06.018 426, 469 (2006);
8. X. W. Hou, J. H. Chen, and B. Hu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.034302 71, 034302 (2005).
9. S. D. Du and C. D. Gong, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.50.779 50, 779 (1994).
10. O. Osenda and P. Serra, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.042331 75, 042331 (2007).
11. V. S. Malinovsky and I. R. Sola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.050502 96, 050502 (2006).
12. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.3824 54, 3824 (1996).
13. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.722 76, 722 (1996).
14. V. Vedral, M. B. Plenio, M. A. Rippin, and P. L. Knight, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.2275 78, 2275 (1997).
15. J. Gong and P. Brumer, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68. 022101 68, 022101 (2003).
16. S. Schneider and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.042107 65, 042107 (2002).
17. W. H. Zurek, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.75.715 75, 715 (2003).
18. H. K. Park and S. W. Kim, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.060102 67, 060102 (R) (2003).
19. M. Hiller, T. Kottos, and A. Ossipov, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.063625 73, 063625 (2006).
20. R. Franzosi and V. Penna, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.043609 63, 043609 (2001);
21. R. Franzosi, V. Penna, and R. Zecchina, Int. J. Mod. Phys. B IJPBEV 0217-9792 10.1142/S0217979200001011 14, 943 (2000).
22. G. Kalosakas, A. R. Bishop, and V. M. Kenkre, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.023602 68, 023602 (2003);
23. G. Kalosakas and A. R. Bishop, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.043616 65, 043616 (2002).
24. M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.010402 95, 010402 (2005).
25. S. Aubry, S. Flach, K. Kladko, and E. Olbrich, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.1607 76, 1607 (1996).
26. C. M. Tesch and R. de Vivie-Riedle, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.157901 89, 157901 (2002).
27. D. Babikor, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1791635 121, 7577 (2004).
28. T. Cheg and A. Brown, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2164457 124, 034111 (2006).
29. M. E. Kellman, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.449095 83, 3843 (1985).
30. P. J. Wang and G. Z. Wu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.022116 66, 022116 (2002).
31. S. Keshavamurthy, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1881152 122, 114109 (2005).
32. J. Zúñiga, J. Antonio, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2743441 126, 244305 (2007).
33. T. Sako, K. Yamanouchi, and F. Iachello, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1368132 114, 9441 (2001).
34. L. Sanz, R. M. Angelo, and K. Furuya, J. Phys. A JPHAC5 0305-4470 36, 9739 (2003).
35. Y. X. Liu, S. K. Özdemir, A. Miranowicz, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/15/010 37, 4423 (2004).
36. M. E. Kellman and V. Tyng, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.013602 66, 013602 (2002).
37. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.53.2046 53, 2046 (1996).
38. A. Isar, Fortschr. Phys. FPYKA6 0015-8208 10.1002/(SICI)1521-3978(199909) 47:7/8<855::AID-PROP855>3.0.CO;2-Z 47, 855 (1999).
39. M. Mirraphimi, G. Turinici, and P. Rouchon, J. Phys. Chem. A JPCAFH 1089-5639 10.1021/jp0472461 109, 2631 (2005).
40. K. Beauchard, J. M. Coron, M. Mirrahimi, and P. Rouchon, Syst. Control Lett. SCLEDC 0167-6911 10.1016/j.sysconle.2006.10.024 56, 388 (2007).
41. M. Mirrahimi and R. V. Handel, SIAM J. Control Optim. SJCODC 0363-0129 10.1137/050644793 46, 445 (2007);
42. M. Mirrahimi, P. Rouchon, and G. Turinici, Automatica ATCAA9 0005-1098 10.1016/j.automatica.2005.05.018 41, 1987 (2005).
43. S. Ceng, Introduction to Quantum Mechanical System Control (Scientific Press, Beijing, 2006).
44. K. Furuya, M. C. Nemes, and G. Q. Pellegrino, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.80.5524 80, 5524 (1998).
45. P. A. Miller and S. Sarkar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.1542 60, 1542 (1999).
46. S. Bettelli and D. L. Shepelyansky, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.054303 67, 054303 (2003).
47. A. Lakshminarayan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64. 036207 64, 036207 (2001).
48. H. Fujisaki, T. Miyadera, and A. Tanaka, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.066201 67, 066201 (2003).
49. A. J. Scott and C. M. Caves, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/36/308 36, 9553 (2003).
50. Ph. Jacquod, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 150403 92, 150403 (2004).
51. X. Wang, S. Ghose, B. C. Sanders, and B. Hu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.016217 70, 016217 (2004).
52. S. Ghose and B. C. Sanders, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.062315 70, 062315 (2004).
53. W. M. Zhang, D. H. Feng, and R. Gilmore, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.62.867 62, 867 (1990).
54. R. Gilmore, Catastrophe Theory for Scientists and Engineers (Wiley, New York, 1981).
55. S. Ding and Y. Zheng, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.479210 111, 4466 (1999);
56. Y. Zheng and S. Ding, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.64. 032720 64, 032720 (2001).