Geodesic
Polarons on the One-Dimensional Lattice in the Su--Schrieffer--Heeger Model. Charge Transfer in~DNA
Matematičeskaâ biologiâ i bioinformatika, Tome 8 (2013) no. 1, pp. 316-339.

Voir la notice de l'article provenant de la source Math-Net.Ru

Polarons on the one-dimensional lattice are thoroughly analyzed. A lattice consists of particles interacting via the nearest-neighbor potential — harmonic or nonlinear. The electron-phonon interaction is accounted in the Su–Shrieffer–Heeger approximation. Initially the unmovable polarons on the harmonic lattice are considered. Analytical expressions for both small and large radii polarons are derived. Solutions for the movable polarons are obtained in the continuous approximation. Their stability is verified in numerical simulation. Exactly integrable equations are also derived with multisoliton solutions. Analytical solutions are obtained for the anharmonic lattice with the potential $U(q)=q_2/2-\beta q_3/3$. Analytical solutions are obtained in the continuum approximation. Stable solutions also exist in the range of parameters where the continuum approximation is invalid. Polarobreathers with the envelope consisting of few peaks are found. The polaron velocity is determined by the concurrence of lattice nonlinearity $\beta$ and the electron-phonon interaction and can exceed the sound velocity. Few particular cases of the polaron evolution on the finite length lattice are considered. An applicability of the considered model to the charge transfer in DNA is briefly analyzed. 
@article{MBB_2013_8_1_a9,
     author = {T. Yu. Astakhova and V. A. Kashin and V. N. Likhachev and G. A. Vinogradov},
     title = {Polarons on the {One-Dimensional} {Lattice} in the {Su--Schrieffer--Heeger} {Model.} {Charge} {Transfer} {in~DNA}},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {316--339},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2013_8_1_a9/}
}
TY  - JOUR
AU  - T. Yu. Astakhova
AU  - V. A. Kashin
AU  - V. N. Likhachev
AU  - G. A. Vinogradov
TI  - Polarons on the One-Dimensional Lattice in the Su--Schrieffer--Heeger Model. Charge Transfer in~DNA
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2013
SP  - 316
EP  - 339
VL  - 8
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2013_8_1_a9/
LA  - ru
ID  - MBB_2013_8_1_a9
ER  - 
%0 Journal Article
%A T. Yu. Astakhova
%A V. A. Kashin
%A V. N. Likhachev
%A G. A. Vinogradov
%T Polarons on the One-Dimensional Lattice in the Su--Schrieffer--Heeger Model. Charge Transfer in~DNA
%J Matematičeskaâ biologiâ i bioinformatika
%D 2013
%P 316-339
%V 8
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2013_8_1_a9/
%G ru
%F MBB_2013_8_1_a9
T. Yu. Astakhova; V. A. Kashin; V. N. Likhachev; G. A. Vinogradov. Polarons on the One-Dimensional Lattice in the Su--Schrieffer--Heeger Model. Charge Transfer in~DNA. Matematičeskaâ biologiâ i bioinformatika, Tome 8 (2013) no. 1, pp. 316-339. http://geodesic.mathdoc.fr/item/MBB_2013_8_1_a9/

[1] Gorodetsky A. A., Buzzeo M. C., Barton J. K., Bioconjugate Chem., 19 (2008), 2285–2296 | DOI

[2] Mallajosyula S. S., Pati S. K., J. Phys. Chem. Lett., 1 (2010), 1881–1894 | DOI

[3] Genereux C. G., Boal A. K., Barton J. K., J. Am. Chem. Soc., 132 (2010), 891–905 | DOI

[4] Cordes M., Giese B., Chem. Soc. Rev., 38 (2009), 892–901 | DOI

[5] Kawai K., Kodera H., Osakada Y., Majima T., Nature Chem., 1 (2009), 156–159 | DOI

[6] Mitra A., Aleiner I., Millis A. J., Phys. Rev. B, 69 (2004), 245302 | DOI

[7] Cornaglia P. S., Grempel D. R., Ness H., Phys. Rev. B, 71 (2005), 075320 | DOI

[8] Nun̄ez Regueiro M. D., Cornaglia P. S., Usaj G., Balseiro C. A., Phys. Rev. B, 76 (2007), 075425 | DOI

[9] Hameau S., Guldner Y., Verzelen O., Ferreira R., Bastard G., Zeman J., Lemaitre A., Gérard J. M., Phys. Rev. Lett., 83 (1999), 4152–4155 | DOI

[10] Muljarov E. A., Zimmermann R., Phys. Rev. Lett., 93 (2004), 237401 | DOI

[11] Hohenadler M., Fehske H. J., Phys. Condens. Matter, 19 (2007), 255210 | DOI

[12] Hohenadler M., Littlewood P. B., Phys. Rev. B, 76 (2007), 155122 | DOI

[13] LeRoy B., Lemay S., Kong J., Dekker C., Nature, 432 (2004), 371–374 | DOI

[14] Shen X. Y., Dong B., Lei X. L., Horing N. J. M., Phys. Rev. B, 76 (2007), 115308 | DOI

[15] Heeger A., Kivelson S., Schrieffer J. R., Su W.-P., Rev. Mod. Phys., 60 (1988), 781–850 | DOI

[16] Gershenson M. E., Podzorov V., Morpurgo A. F., Rev. Mod. Phys., 78 (2006), 973–989 | DOI

[17] Coropceanu V., Cornil J., da Silva D. A., Olivier Y., Silbey R., Brédas J., Chem. Rev., 107 (2007), 926–952 | DOI

[18] Grozema F., Siebbeles L. D. A., Int. Rev. Phys. Chem., 27 (2008), 87–138 | DOI

[19] Ortmann F., Bechstedt F., Hannewald K., New J. Phys., 12 (2010), 023011 | DOI

[20] Stafström S., Chem. Soc. Rev., 39 (2010), 2484–2499 | DOI

[21] Lakhno V. D., Solid State Commun., 152 (2012), 621–623 | DOI

[22] Bussmann-Holder A., Keller H., de Leon J. M., Simon A., Bishop A. R., Muller K. A., J. Superconductivity Novel Magnetism, 23 (2010), 295–299 | DOI

[23] Lee B. S., J. Superconductivity Novel Magnetism, 23 (2010), 333–338 | DOI

[24] Bussmann-Holder A., Keller H. J., Superconductivity Novel Magnetism, 22 (2009), 123–129 | DOI

[25] Genereux J. C., Barton J. K., Chem. Rev., 110 (2010), 1642–1662 | DOI

[26] Genereux J. C., Wuerth S. M., Barton J. K., J. Am. Chem. Soc., 133 (2011), 3863–3868 | DOI

[27] Arikuma Y., Nakayama H., Morita T., Kimura S., Angew. Chem. Int. Ed., 49 (2010), 1800–1804 | DOI

[28] Augustyn K. E., Genereux J. C., Barton J. K., Angew. Chem. Int. Ed., 46 (2007), 5731–5733 | DOI

[29] Barton J. K., Olmon E. D., Sontz P. A., Coordin. Chem. Rev., 255 (2011), 619–634 | DOI

[30] Slinker J. D., Muren N. B., Renfrew S. E., Barton J. K., Nature Chemistry, 3 (2011), 228–233 | DOI

[31] Astakhova T. Yu., Likhachev V. N., Vinogradov G. A., Uspekhi khimii, 81 (2012), 994–1010

[32] Lakhno V. D., Intern. J. Quant. Chem., 110 (2010), 127–137 | DOI

[33] Holstein T., Ann. Phys., 8 (1959), 325–342 | DOI | Zbl

[34] Su W. P., Schrieffer J. R., Heeger A. J., Phys. Rev. Lett., 42 (1979), 1698–1701 | DOI

[35] Mozafari E., Stafström S., Phys. Lett. A, 376 (2012), 1807–1811 | DOI

[36] Maniadis P., Kalosakas G., Rasmussen K.Ø., Bishop A. R., Phys. Rev. B, 68 (2003), 174304 | DOI | MR

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

[38] Iguchi K., Int. J. Mod. Phys. B, 17 (2003), 2565–3578 | DOI

[39] Lakhno V. D., Physics of Particles and Nuclei Letters, 5 (2008), 231–235 | DOI

[40] Wang Y., Fu L., Wang K.-L., Biophisical Chemistry, 119 (2006), 107–114 | DOI

[41] Conwell E. M., Rakhmanova S. V., Proc. Natl. Acad. Sci. USA, 97 (2000), 4556–4560 | DOI

[42] Conwell E. M., Basko D. M., J. Am. Chem. Soc., 123 (2001), 11441–11445 | DOI

[43] Conwell E. M., Proc. Natl. Acad. Sci. USA, 102 (2005), 8795–8799 | DOI

[44] Kalosakas G., Aubry S., Tsironis G. P., Phys. Rev. B, 58 (1998), 3094–3104 | DOI

[45] Dubrovin B. A., Malanyuk T. M., Krichever I. M., Makhankov V. G., Fizika elementarnykh chastits i atomnogo yadra, 19 (1988), 579–621 | MR

[46] Sasaki K., Progr. Theor. Phys., 65 (1981), 1787–1797 | DOI

[47] Leblond H. J., Phys. B, 41 (2008), 043001 | DOI | MR

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

[49] Remoissenet M., Waves Called Solitons. Concepts and Experiment, Springer, Berlin, 1996, 260 pp. | MR | Zbl

[50] Kalosakas G., Aubry S., Physica D, 113 (1998), 228–232 | DOI | Zbl

[51] Cuevas J., Kevrekidis P. G., Frantzeskakis D. J., Bishop A. R., Phys. Rev. B, 74 (2006), 064304 | DOI

[52] Aubry S., Polarons in Advanced Materials, Springer Series in Materials Science, 103, 2007, 311–371 | DOI

[53] Cruzeiro-Hansson L., Eilbeck J. C., Marin J. L., Russell F. M., Physica D, 142 (2000), 101–112 | DOI | Zbl

[54] Lakhno V. D., Korshunova A. N., Matematicheskaya biologiya i bioinformatika, 5 (2010), 29 pp. (data obrascheniya: 20.05.2013) http://www.matbio.org/downloads_en/Lakhno_en2010(5_1).pdf

[55] Fehske H., Wellein G., Bishop A. R., Phys. Rev. B, 83 (2011), 075104 | DOI

[56] Wu J. A., Walker V. E. J., Boyd R. J., J. Phys. Chem. B, 115 (2011), 3136–3145 | DOI

[57] Wu C. Q., Qiu Y., An Z., Nasu K., Phys. Rev. B, 68 (2003), 125416 | DOI

[58] Li G., Movaghar B., Ratner M. A., Phys. Rev. B, 87 (2013), 094302 | DOI

[59] Li G., Movaghar B., Nitzan A., Ratner M. A., J. Chem. Phys., 138 (2013), 044112 | DOI

[60] Likhachev V. N., Astakhova T. Yu., Vinogradov G. A., Cornell University Library, arXiv: 1302.2777

[61] Likhachev V. N., Astakhova T. Yu., Vinogradov G. A., Cornell University Library, arXiv: 1302.2779