Davydov model: The quantum, mixed quantum-classical, and full classical systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 56, Issue 1 SUPPL. B, 1997, Pages 894-906

  Cruzeiro Hansson, Leonor ^a   Takeno, Shozo ^b  

^a UNIVERSITY OF LONDON   (United Kingdom)

^b OSAKA INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000722340     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.56.894     Document Type: Article

References (76)

1. A. S. Davydov, J. Theor. Biol. 38, 559 (1973); 66, 379 (1977); Int. J. Quantum Chem. 16, 5 (1979): Biology and Quantum Mechanics (Pergamon, New York, 1982); Physica D 3, 1 (1981); Usp. Fiz. Nauk 138, 603 (1982) [Sov. Phys. Usp. 25, 898 (1982)]; L. S. Brizhik and A. S. Davydov. Phys. Status Solidi B 115, 615 (1983).
2. A. S. Davydov, J. Theor. Biol. 38, 559 (1973); 66, 379 (1977); Int. J. Quantum Chem. 16, 5 (1979): Biology and Quantum Mechanics (Pergamon, New York, 1982); Physica D 3, 1 (1981); Usp. Fiz. Nauk 138, 603 (1982) [Sov. Phys. Usp. 25, 898 (1982)]; L. S. Brizhik and A. S. Davydov. Phys. Status Solidi B 115, 615 (1983).
3. A. S. Davydov, J. Theor. Biol. 38, 559 (1973); 66, 379 (1977); Int. J. Quantum Chem. 16, 5 (1979): Biology and Quantum Mechanics (Pergamon, New York, 1982); Physica D 3, 1 (1981); Usp. Fiz. Nauk 138, 603 (1982) [Sov. Phys. Usp. 25, 898 (1982)]; L. S. Brizhik and A. S. Davydov. Phys. Status Solidi B 115, 615 (1983).
4. A. S. Davydov, J. Theor. Biol. 38, 559 (1973); 66, 379 (1977); Int. J. Quantum Chem. 16, 5 (1979): Biology and Quantum Mechanics (Pergamon, New York, 1982); Physica D 3, 1 (1981); Usp. Fiz. Nauk 138, 603 (1982) [Sov. Phys. Usp. 25, 898 (1982)]; L. S. Brizhik and A. S. Davydov. Phys. Status Solidi B 115, 615 (1983).
5. A. S. Davydov, J. Theor. Biol. 38, 559 (1973); 66, 379 (1977); Int. J. Quantum Chem. 16, 5 (1979): Biology and Quantum Mechanics (Pergamon, New York, 1982); Physica D 3, 1 (1981); Usp. Fiz. Nauk 138, 603 (1982) [Sov. Phys. Usp. 25, 898 (1982)]; L. S. Brizhik and A. S. Davydov. Phys. Status Solidi B 115, 615 (1983).
6. A. S. Davydov, J. Theor. Biol. 38, 559 (1973); 66, 379 (1977); Int. J. Quantum Chem. 16, 5 (1979): Biology and Quantum Mechanics (Pergamon, New York, 1982); Physica D 3, 1 (1981); Usp. Fiz. Nauk 138, 603 (1982) [Sov. Phys. Usp. 25, 898 (1982)]; L. S. Brizhik and A. S. Davydov. Phys. Status Solidi B 115, 615 (1983).
7. A. S. Davydov, J. Theor. Biol. 38, 559 (1973); 66, 379 (1977); Int. J. Quantum Chem. 16, 5 (1979): Biology and Quantum Mechanics (Pergamon, New York, 1982); Physica D 3, 1 (1981); Usp. Fiz. Nauk 138, 603 (1982) [Sov. Phys. Usp. 25, 898 (1982)]; L. S. Brizhik and A. S. Davydov. Phys. Status Solidi B 115, 615 (1983).
8. A. S. Davydov, J. Theor. Biol. 38, 559 (1973); 66, 379 (1977); Int. J. Quantum Chem. 16, 5 (1979): Biology and Quantum Mechanics (Pergamon, New York, 1982); Physica D 3, 1 (1981); Usp. Fiz. Nauk 138, 603 (1982) [Sov. Phys. Usp. 25, 898 (1982)]; L. S. Brizhik and A. S. Davydov. Phys. Status Solidi B 115, 615 (1983).
9. A. Scott, Phys. Rep. 217, 1 (1992).
10. D. Kapor, M. Skrinjar, Z. Ivic, and Z. Przulj, Bioelectrochem. Bioenerg. 41, 93 (1996); Z. Ivic, Z. Przulj, D. Kapor, and M. Skrinjar, ibid. 41, 43 (1996); Z. Ivic, Z. Przulj, D. Kostic, D. Kapor, and M. Skrinjar, Phys. Rev. B 54, 2992 (1996).
11. D. Kapor, M. Skrinjar, Z. Ivic, and Z. Przulj, Bioelectrochem. Bioenerg. 41, 93 (1996); Z. Ivic, Z. Przulj, D. Kapor, and M. Skrinjar, ibid. 41, 43 (1996); Z. Ivic, Z. Przulj, D. Kostic, D. Kapor, and M. Skrinjar, Phys. Rev. B 54, 2992 (1996).
12. D. Kapor, M. Skrinjar, Z. Ivic, and Z. Przulj, Bioelectrochem. Bioenerg. 41, 93 (1996); Z. Ivic, Z. Przulj, D. Kapor, and M. Skrinjar, ibid. 41, 43 (1996); Z. Ivic, Z. Przulj, D. Kostic, D. Kapor, and M. Skrinjar, Phys. Rev. B 54, 2992 (1996).
13. W. Förner, J. Mol. Model. 2, 70 (1996); 2, 103 (1996); Phys. Rev. B 53, 6291 (1996).
14. W. Förner, J. Mol. Model. 2, 70 (1996); 2, 103 (1996); Phys. Rev. B 53, 6291 (1996).
15. W. Förner, J. Mol. Model. 2, 70 (1996); 2, 103 (1996); Phys. Rev. B 53, 6291 (1996).
16. V. M. Kenkre, S. Raghavan, A. R. Bishop, and M. I. Salkola, Phys. Rev. B 53, 5407 (1996); S. Raghavan, V. M. Kenkre, A. R. Bishop, and M. I. Salkola, ibid. 53, 8457 (1996).
17. V. M. Kenkre, S. Raghavan, A. R. Bishop, and M. I. Salkola, Phys. Rev. B 53, 5407 (1996); S. Raghavan, V. M. Kenkre, A. R. Bishop, and M. I. Salkola, ibid. 53, 8457 (1996).
18. A. V. Zolotariuk, K. H. Spatschek, and A. V. Savin, Phys. Rev. B 54, 266 (1996); Europhys. Lett. 31, 531 (1995).
19. A. V. Zolotariuk, K. H. Spatschek, and A. V. Savin, Phys. Rev. B 54, 266 (1996); Europhys. Lett. 31, 531 (1995).
20. M. Daniel and K. Deepamala, Physica A 221, 241 (1995); E. A. Bartnik, J. A. Tuszynski, and D. Sept, Phys. Lett. A 204, 263 (1995); D. Todorovic, L. Ristovski, and B. S. Tosic, Phys. Status Solidi B 190, 251 (1995); H. Rosu, Nuovo Cimento D 18, 477 (1996).
21. M. Daniel and K. Deepamala, Physica A 221, 241 (1995); E. A. Bartnik, J. A. Tuszynski, and D. Sept, Phys. Lett. A 204, 263 (1995); D. Todorovic, L. Ristovski, and B. S. Tosic, Phys. Status Solidi B 190, 251 (1995); H. Rosu, Nuovo Cimento D 18, 477 (1996).
22. M. Daniel and K. Deepamala, Physica A 221, 241 (1995); E. A. Bartnik, J. A. Tuszynski, and D. Sept, Phys. Lett. A 204, 263 (1995); D. Todorovic, L. Ristovski, and B. S. Tosic, Phys. Status Solidi B 190, 251 (1995); H. Rosu, Nuovo Cimento D 18, 477 (1996).
23. M. Daniel and K. Deepamala, Physica A 221, 241 (1995); E. A. Bartnik, J. A. Tuszynski, and D. Sept, Phys. Lett. A 204, 263 (1995); D. Todorovic, L. Ristovski, and B. S. Tosic, Phys. Status Solidi B 190, 251 (1995); H. Rosu, Nuovo Cimento D 18, 477 (1996).
24. There are several ways of quantizing systems. Here we consider the following way: The quantum correspondent of a classical displacement u, the classical momentum p, and the classical complex amplitude a∝X+ip are. respectively, the displacement operator Û, the quantum momentum operator P̂, and the annihilation operator Â.
25. L. Cruzeiro-Hansson, Europhys. Lett. 33, 655 (1996).
26. L. Cruzeiro-Hansson, Phys. Lett. A 223, 383 (1996).
27. X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. Lett. 62, 1796 (1989); in Davydov's Soliton Revisited, edited by P. L. Christiansen and A. C. Scott (Plenum. New York, 1990).
28. X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. Lett. 62, 1796 (1989); in Davydov's Soliton Revisited, edited by P. L. Christiansen and A. C. Scott (Plenum. New York, 1990).
29. R. P. Feynman, Statistical Mechanics (Benjamin, Reading, MA, 1972).
30. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
31. L. Cruzeiro-Hansson and V. M. Kenkre, Phys. Lett. A 203, 362 (1995).
32. L. Cruzeiro-Hansson, Phys. Rev. A 45, 4111 (1992).
33. J. M. Hyman, D. W. McLaughlin, and A. C. Scott, Physica D 3, 23 (1981); A. C. Scott. Phys. Scr. 29, 279 (1984); L. Mac-Neil and A. C. Scott, ibid. 29, 284 (1981).
34. J. M. Hyman, D. W. McLaughlin, and A. C. Scott, Physica D 3, 23 (1981); A. C. Scott. Phys. Scr. 29, 279 (1984); L. Mac-Neil and A. C. Scott, ibid. 29, 284 (1981).
35. J. M. Hyman, D. W. McLaughlin, and A. C. Scott, Physica D 3, 23 (1981); A. C. Scott. Phys. Scr. 29, 279 (1984); L. Mac-Neil and A. C. Scott, ibid. 29, 284 (1981).
36. G. P. Tsironis and V. M. Kenkre, Phys. Lett. A 127, 209 (1988); V. M. Kenkre and H.-L. Wu, ibid. 135, 120 (1989).
37. G. P. Tsironis and V. M. Kenkre, Phys. Lett. A 127, 209 (1988); V. M. Kenkre and H.-L. Wu, ibid. 135, 120 (1989).
38. P. W. Miloni, J. R. Ackerhalt, and H. R. Galbraith, Phys. Rev. Lett. 50, 966 (1983); D. Feinberg and J. Ranninger, Physica D 14, 29 (1984).
39. P. W. Miloni, J. R. Ackerhalt, and H. R. Galbraith, Phys. Rev. Lett. 50, 966 (1983); D. Feinberg and J. Ranninger, Physica D 14, 29 (1984).
40. P. S. Lomdahl and W. C. Kerr, Phys. Rev. Lett. 55, 1235 (1985).
41. S. Nosé, Mol. Phys. 52, 255 (1984); W. G. Hoover, Phys. Rev. A 31, 1695 (1985); S. Nosé, Prog. Theor. Phys. Suppl. 103. 1 (1991).
42. S. Nosé, Mol. Phys. 52, 255 (1984); W. G. Hoover, Phys. Rev. A 31, 1695 (1985); S. Nosé, Prog. Theor. Phys. Suppl. 103. 1 (1991).
43. S. Nosé, Mol. Phys. 52, 255 (1984); W. G. Hoover, Phys. Rev. A 31, 1695 (1985); S. Nosé, Prog. Theor. Phys. Suppl. 103. 1 (1991).
44. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
45. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
46. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
47. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
48. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
49. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
50. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
51. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
52. W. Förner, J. Phys. Condens. Matter 3, 3235 (1991); 3, 4333 (1991); Phys. Rev. A 44, 2694 (1991); J. Phys. Condens. Matter 4, 1915 (1992); J. Comput. Chem. 13, 275 (1992); J. Phys. Condens. Matter 5, 803 (1993); 5, 823 (1993); 5, 3883 (1993); 5, 3897 (1993).
53. L. Cruzeiro-Hansson, V. A. Okhonin, R. G. Khlebopros, and I. N. Yassievich, Nanobiology 1, 395 (1992).
54. F. Mauri, R. Car, and E. Tosatti, Europhys. Lett. 24, 431 (1993).
55. V. M. Kenkre and P. Grigolini, Z. Phys. B 90, 247 (1993).
56. L. Cruzeiro-Hansson, Physica D 68, 65 (1993).
57. J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Physica D 16, 318 (1985); A. C. Scott, E. Gratton, E. Shyamsunder. and G. Careri, Phys. Rev. B 32, 5551 (1985).
58. J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Physica D 16, 318 (1985); A. C. Scott, E. Gratton, E. Shyamsunder. and G. Careri, Phys. Rev. B 32, 5551 (1985).
59. n}. Comparisons between regimes should be made by comparing measurable quantities.
60. L. Bonci, P. Grigolini, and D. Vitali, Phys. Rev. A 42, 4452 (1990); D. Vitali, L. Bonci, R. Mannella, and P. Grigolini, ibid. 45, 2285 (1992); L. Bonci, and P. Grigolini, ibid. 46, 4445 (1992).
61. L. Bonci, P. Grigolini, and D. Vitali, Phys. Rev. A 42, 4452 (1990); D. Vitali, L. Bonci, R. Mannella, and P. Grigolini, ibid. 45, 2285 (1992); L. Bonci, and P. Grigolini, ibid. 46, 4445 (1992).
62. L. Bonci, P. Grigolini, and D. Vitali, Phys. Rev. A 42, 4452 (1990); D. Vitali, L. Bonci, R. Mannella, and P. Grigolini, ibid. 45, 2285 (1992); L. Bonci, and P. Grigolini, ibid. 46, 4445 (1992).
63. G. Careri, U. Buontempo, F. Carta, E. Gratton, and A. C. ott, Phys. Rev. Lett. 51, 304 (1983); J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Phys. Rev. B 30, 4703 (1984); G. Careri, U. Buontempo, F. Galluzzi, A. C. Scott, E. Gratton, and E. Shyamsunder, ibid. 30, 4689 (1984); G. Careri, E. Gratton, and E. Shyamsunder, Phys. Rev. A 37, 4048 (1988).
64. G. Careri, U. Buontempo, F. Carta, E. Gratton, and A. C. ott, Phys. Rev. Lett. 51, 304 (1983); J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Phys. Rev. B 30, 4703 (1984); G. Careri, U. Buontempo, F. Galluzzi, A. C. Scott, E. Gratton, and E. Shyamsunder, ibid. 30, 4689 (1984); G. Careri, E. Gratton, and E. Shyamsunder, Phys. Rev. A 37, 4048 (1988).
65. G. Careri, U. Buontempo, F. Carta, E. Gratton, and A. C. ott, Phys. Rev. Lett. 51, 304 (1983); J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Phys. Rev. B 30, 4703 (1984); G. Careri, U. Buontempo, F. Galluzzi, A. C. Scott, E. Gratton, and E. Shyamsunder, ibid. 30, 4689 (1984); G. Careri, E. Gratton, and E. Shyamsunder, Phys. Rev. A 37, 4048 (1988).
66. G. Careri, U. Buontempo, F. Carta, E. Gratton, and A. C. ott, Phys. Rev. Lett. 51, 304 (1983); J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Phys. Rev. B 30, 4703 (1984); G. Careri, U. Buontempo, F. Galluzzi, A. C. Scott, E. Gratton, and E. Shyamsunder, ibid. 30, 4689 (1984); G. Careri, E. Gratton, and E. Shyamsunder, Phys. Rev. A 37, 4048 (1988).
67. W. Fann, L. Rothberg, M. Robertson, S. Benson, J. Madey, S. Etemad, and R. Austin, Phys. Rev. Lett. 64, 607 (1990); T. Rozgonyi, and A. Lörincz, J. Appl. Phys. 75, 1861 (1994).
68. W. Fann, L. Rothberg, M. Robertson, S. Benson, J. Madey, S. Etemad, and R. Austin, Phys. Rev. Lett. 64, 607 (1990); T. Rozgonyi, and A. Lörincz, J. Appl. Phys. 75, 1861 (1994).
69. S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984); 73, 853 (1985); in Computer Analysis for Life Science, edited by C. Kawabata and A. R. Bishop (Ohmsha, Tokyo, 1985), p. 47; Prog. Theor. Phys. 75, 1 (1986); J. Phys. Soc. Jpn. 58, 1639 (1989); 59, 3127 (1990); X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. B 39, 5366 (1989).
70. S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984); 73, 853 (1985); in Computer Analysis for Life Science, edited by C. Kawabata and A. R. Bishop (Ohmsha, Tokyo, 1985), p. 47; Prog. Theor. Phys. 75, 1 (1986); J. Phys. Soc. Jpn. 58, 1639 (1989); 59, 3127 (1990); X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. B 39, 5366 (1989).
71. S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984); 73, 853 (1985); in Computer Analysis for Life Science, edited by C. Kawabata and A. R. Bishop (Ohmsha, Tokyo, 1985), p. 47; Prog. Theor. Phys. 75, 1 (1986); J. Phys. Soc. Jpn. 58, 1639 (1989); 59, 3127 (1990); X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. B 39, 5366 (1989).
72. S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984); 73, 853 (1985); in Computer Analysis for Life Science, edited by C. Kawabata and A. R. Bishop (Ohmsha, Tokyo, 1985), p. 47; Prog. Theor. Phys. 75, 1 (1986); J. Phys. Soc. Jpn. 58, 1639 (1989); 59, 3127 (1990); X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. B 39, 5366 (1989).
73. S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984); 73, 853 (1985); in Computer Analysis for Life Science, edited by C. Kawabata and A. R. Bishop (Ohmsha, Tokyo, 1985), p. 47; Prog. Theor. Phys. 75, 1 (1986); J. Phys. Soc. Jpn. 58, 1639 (1989); 59, 3127 (1990); X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. B 39, 5366 (1989).
74. S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984); 73, 853 (1985); in Computer Analysis for Life Science, edited by C. Kawabata and A. R. Bishop (Ohmsha, Tokyo, 1985), p. 47; Prog. Theor. Phys. 75, 1 (1986); J. Phys. Soc. Jpn. 58, 1639 (1989); 59, 3127 (1990); X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. B 39, 5366 (1989).
75. S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984); 73, 853 (1985); in Computer Analysis for Life Science, edited by C. Kawabata and A. R. Bishop (Ohmsha, Tokyo, 1985), p. 47; Prog. Theor. Phys. 75, 1 (1986); J. Phys. Soc. Jpn. 58, 1639 (1989); 59, 3127 (1990); X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. B 39, 5366 (1989).
76. S. Takeno, Prog. Theor. Phys. 69, 1798 (1983); 71, 395 (1984); 73, 853 (1985); in Computer Analysis for Life Science, edited by C. Kawabata and A. R. Bishop (Ohmsha, Tokyo, 1985), p. 47; Prog. Theor. Phys. 75, 1 (1986); J. Phys. Soc. Jpn. 58, 1639 (1989); 59, 3127 (1990); X. Wang, D. W. Brown, and K. Lindenberg, Phys. Rev. B 39, 5366 (1989).