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The unified theory of Davydov's and Fröhlich's models

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Zeitschrift für Physik B Condensed Matter

Abstract

Starting from the experimental facts and from quite general theoretical assumptions a theoretical model was formulated and the Hamiltonian derived which describes the possible excitations in a biological system. Davydov's and Fröhlich's models are also devoted to the same problem, although it seems that these models are not connected. Our results show that the Hamiltonians of Davydov's and Fröhlich's models can be easily obtained from the Hamiltonian of our model. More precisely, our theory could be considered as the microscopic theory of Fröhlich's model, from which Davydov's theoretical model follows as a particular case.

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References

  1. Davydov, A.S.: Biology and quantum mechanics. New York: Pergamon Press 1982

    Google Scholar 

  2. Pretrov, E.G.: Physics of charge transfer in biological systems. Moscow: Naukova Dumka, 1984 [in Russian]

    Google Scholar 

  3. Kalous, V., Pavlicek, Z.: Biofyzikalni chemie. Praha: SNTL 1980 [or Russian translation Mir 1984]

    Google Scholar 

  4. Lewis, T.: Phys. Med. Biol.27, 335 (1982)

    Google Scholar 

  5. Bone, S., Pething, R.: Submolecular Biology and Cancer. Basel: Ciba Foundation 1979, Ser. 67, pp. 882–305

    Google Scholar 

  6. Davydov, A.S.: Stud. Biophys.62, 1 (1977)

    Google Scholar 

  7. Davydov, A.S.: Phys. Scr.20, 387 (1979)

    Google Scholar 

  8. Davydov, A.S.: Usp. Fiz. Nauk138, 603 (1982)

    Google Scholar 

  9. Davydov, A.S.: Solitons in molecular systems. Moscow: Naukova Dumka 1984 [in Russian]

    Google Scholar 

  10. Bolterauer, H.: Proc. from MIDIT Workshop 1986

  11. Bolterauer, H., Henkel, R.D., Opper, M.: Proc. from MIDIT Workshop 1986

  12. Scott, A.C.: Phys. Rev. A26, 578 (1982)

    Google Scholar 

  13. Scott, A.C.: Phys. Scr.25, 651 (1982)

    Google Scholar 

  14. Scott, A.C.: Phys. Lett. A94, 193 (1983)

    Google Scholar 

  15. Scott, A.C.: Phys. Scr.29, 279 (1984)

    Google Scholar 

  16. Lawrence, A.F., et al.: Phys. Rev. A33, 1188 (1986)

    Google Scholar 

  17. Fröhlich, H.: Int. J. Quantum Chem.2, 641 (1968)

    Google Scholar 

  18. Fröhlich, H.: Phys. Lett. A26, 402 (1968)

    Google Scholar 

  19. Fröhlich, H.: Phys. Lett. A39, 153 (1972)

    Google Scholar 

  20. Fröhlich, H.: Proc. Natl. Acad. Sci. USA72, 4211 (1975)

    Google Scholar 

  21. Bhaumik, D., et al.: Phys. Lett. A62, 72 (1977)

    Google Scholar 

  22. Bhaumik, D., Dutta-Roy, B., Lahiri, A.: Phys. Lett. A68, 131 (1978)

    Google Scholar 

  23. Bhaumik, D., Dutta-Roy, B., Lahiri, A.: Phys. Lett A69, 68 (1978)

    Google Scholar 

  24. Wu, T.M., Austin, S.: Phys. Lett. A64, 151 (1977)

    Google Scholar 

  25. Wu, T.M., Austin, S.: Phys. Lett. A65, 74 (1978)

    Google Scholar 

  26. Wu, T.M., Austin, S.: Phys. Lett. A73, 266 (1979)

    Google Scholar 

  27. Takeno, S.: Prog. Theor. Phys.71, 395 (1984)

    Google Scholar 

  28. Takeno, S.: Prog. Theor. Phys.73, 853 (1985)

    Google Scholar 

  29. Takeno, S.: Prog. Theor. Phys.75, 1 (1986)

    Google Scholar 

  30. Tuszynski, J.A., et al.: Phys. Rev. A30, 2666 (1984)

    Google Scholar 

  31. Mills, R.E.: Phys. Rev. A43, 3176 (1991)

    Google Scholar 

  32. Tuszynski, J.A., Paul, R.: Phys. Rev. A43, 3179 (1991)

    Google Scholar 

  33. Bolterauer, H., Tuszynski, J.A.: J. Biol. Phys.17, 41 (1989)

    Google Scholar 

  34. Bolterauer, H., Tuszynski, J.A.: Phys. Rev. A44, 1366 (1991)

    Google Scholar 

  35. Agranovich, V.M., Galanin, M.D.: Transport of energy of electronic excitations in condensed media. Moscow: Nauka 1978 [in Russian]

    Google Scholar 

  36. Davydov, A.S.: Theory of molecular excitons. New York: Plenum Press 1971

    Google Scholar 

  37. Agranovic, V.M.: Theory of excitons. Moscow: Nauka 1968 [in Russian]

    Google Scholar 

  38. Stojanović, S.D., et al.: Phys. Status Solidi B79, 433 (1977)

    Google Scholar 

  39. Davydov, A.S., Serivkov, A.A.: Phys. Status Solidi B42, 603 (1970)

    Google Scholar 

  40. Davydov, A.S., Serikov, A.A.: Phys. Status Solidi B44, 127 (1971)

    Google Scholar 

  41. Davydov, A.S., Serikov, A.A.: Excitons in molecular crystals. Mowcow: Naukova Dumka 1973 [in Russian]

    Google Scholar 

  42. Bersuker, I.B., Polinger, V.Z.: Vibronic interactions in the molecules and crystals. Moscow: Nauka, 1983 [in Russian]

    Google Scholar 

  43. Davydov, A.S.: Solid state theory. Moscow: Nauka 1976 [in Russian]

    Google Scholar 

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Ristovski, L.M., Nestorović, N. & Davidović, G.S. The unified theory of Davydov's and Fröhlich's models. Z. Physik B - Condensed Matter 88, 145–157 (1992). https://doi.org/10.1007/BF01323566

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  • DOI: https://doi.org/10.1007/BF01323566

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