Geodesic
Formation of stationary electronic states in finite homogeneous molecular chains
Matematičeskaâ biologiâ i bioinformatika, Tome 5 (2010) no. 1, pp. 1-29.

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Evolution of an arbitrary initial distribution of a quantum-mechanical particle in a uniform molecular chain is simulated by a system of coupled quantumclassical dynamical equations with dissipation. Stability of a uniform distribution of the particle over the chain is studied. An asymptotical expression is obtained for the time in which a localized state is formed. The validity of the expression is checked by direct computational experiments. It is shown that the time of soliton and multisoliton type states formation depends strongly on the initial phase of the particle's wave function. It is shown that in multisoliton states objects with a fractional electron charge which can be observed experimentally are realized. The results obtained are applied to synthetic uniform polynucleotide molecular chains. 
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V. D. Lakhno; A. N. Korshounova. Formation of stationary electronic states in finite homogeneous molecular chains. Matematičeskaâ biologiâ i bioinformatika, Tome 5 (2010) no. 1, pp. 1-29. http://geodesic.mathdoc.fr/item/MBB_2010_5_1_a1/

[1] Dekker C., Ratner M. A., Phys. World, 14 (2001), 29–34

[2] Boon E. M., Barton J. K., Curr. Op. in Struct. Biol., 12 (2002), 320–329 | DOI

[3] Schuster G. B. (ed.), Topics in Current Chemistry, 236/237, Springer-Verlag, Berlin, 2004

[4] Keren K., Berman R. S., Buchstab E., Sivan U. and Braun E., Science, 302 (2003), 1380–1382 | DOI

[5] Lakhno V. D., International Journal of Quantum Chemistry, 108 (2008), 1970–1981 | DOI

[6] Lakhno V. D., J. Biol. Phys., 26 (2000), 133–147 | DOI

[7] Lakhno V. D., Fialko N. S., R and C Dynamics, 7 (2002), 299–313 | DOI | MR | Zbl

[8] Conwell E. M., Rakhmanova S. V., Proc. Natl. Sci. U.S.A, 97 (2000), 4556–4560 | DOI

[9] Lakhno V. D., Fialko N. S., Phys. Lett. A, 278 (2000), 108–111 | DOI

[10] Alexandre S. S., Artacho E., Soler J. M. and Chacham H., Phys. Rev. Lett., 91 (2003), 108105, 4 pp. | DOI

[11] Bernasconi J., Schneider T. (ed.), Physics in one dimension, Springer-Verlag, Berlin, 1981 | MR

[12] Davydov A. S., Sov. Phys. Usp., 138 (1982), 603–643 | MR

[13] Heeger A. J., Kivelson S. and Schrieffer J. R., Rev. Mod. Phys., 60 (1988), 781–850 | DOI

[14] Scott A., Phys. Rep., 217 (1992), 1–67 | DOI

[15] Okahata Y., Kobayashi T., Tanaka K. and Shimomura M. J., Am. Chem. Soc., 120 (1992), 6165–6166 | DOI

[16] Korshunova A. N., Lakhno V. D., Mathematical Modeling, 19 (2007), 3–13 | Zbl

[17] Lakhno V. D., Korshunova A. N., Nelineynaya Dinamika, 4 (2008), 193–214

[18] Jian-Xin Zhu, Rasmussen K. O., Balatsky A. V. and Bishop A. R., J. Phys.: Condens. Matter., 19 (2008), 136203–136211

[19] Kevrekidis P. G., Rasmussen K. O. and Bisop A. R., Int. J. Modern Phys. B, 15 (2001), 2833–2900 | DOI

[20] Flach S., Mackay R. S. (eds.), Physica D., 119, Special volume: Localization in Nonlinear Lattices. Amsterdam: Elsevier (1998) | MR

[21] Starikov E. B., Lewis J. P. and Tanaka S. (eds.), Modern Methods for Theoretical Physical Chemistry of Biopolymers, 2006

[22] Berashevich J. A., Bookatz A. D. and Chakraborty T., J. Phys.: Condens. Matter., 20 (2008), 035207, 5 pp. | DOI

[23] Peyrard M., Nonlinearity, 17 (2004), R1–R40 | DOI | MR | Zbl

[24] Scott A., Phys. Rep., 217 (1992), 1–67 | DOI

[25] Kivshar Y. S., Agrawal G. P., Optical Solitons. From Fibers to Photonic Crystals, Academic Press, New York, 2003, 540 pp.

[26] Akhmediev N. N., Ankiewicz A., Solitons: nonlinear pulses and beams, Chapman and Hall., London, 1997, 335 pp.

[27] Bountis (ed.), “Collective Proton Transport in Hydrogen Bounded System”, Proc. of the NATO Advanced Research Workshop (Heraclion, Crete), Plenum, New York, 1991

[28] Akhmediev N., Ankiewicz A. (eds.), Dissipative Solitons, Lecture Notes in Physics, 661, Spinger, Berlin, 2005, 448 pp. | MR

[29] Holstein T., Ann. Phys., 8 (1959), 343–389 | DOI | Zbl

[30] Lakhno V. D. and Fialko N. S., Eur. Phys. J. B., 43 (2005), 279–281 | DOI

[31] Carr L. D., Clark C. W. and Reinhardt W. P., Phys. Rev. A, 62 (2000), 063610, 10 pp. | DOI

[32] Carr L. D., Clark C. W. and Reinhardt W. P., Phys. Rev. A, 62 (2000), 063611, 10 pp. | DOI

[33] Vansant P., Smondyrev M. A., Peeters F. M. and Devreese J. T., Zeitschrift Fur Physik B, 99 (1996), 345–351 | DOI

[34] Starikov E. B., Phil. Mag., 85 (2005), 3435–3462 | DOI

[35] Porath D., Bezryadin A., de Vries S. and Dekker C., Nature, 403 (2000), 635–638 | DOI

[36] Davydov A. S., Kislukha N. I., Sov. Phys. JETP, 44 (1976), 571–575

[37] Davydov A. S., Sov. Phys. Usp., 25 (1982), 898–918 | DOI | MR

[38] Hennig D., Chetverikov A. P., Velarde M. G. and Ebeling W., Phys. Rev. E, 76 (2007), 046602, 9 pp. | DOI

[39] Lakhno V. D., Modern Methods for Theoretical Physical Chemistry of Biopolymers, eds. Starikov E. B., Lewis J. P. and Tanaka S., Elsevier, Amsterdam, 2006, 461–481

[40] Bykov V. P., Uspekhi Fizicheskikh Nauk, 176 (2006), 1007–1014 | DOI

[41] Kivshar Y. S. and Peyerard M., Phys. Rev. A, 46 (1992), 3198–3205 | DOI