Abstract
Electron trapping by soliton-like (traveling) localized excitations in one-dimensional anharmonic lattices is discussed with particular emphasis on the case of an initially completely delocalized electron.
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References
N.J. Zabusky, M.D. Kruskal, Phys. Rev. Lett. 15, 57 (1965)
M. Toda, Theory of Nonlinear Lattices, 2nd. edn. (Springer, Berlin, 1988)
P.M. Morse, Phys. Rev. 34, 57 (1929)
J. Dancz, S.A. Rice, J. Chem. Phys. 67, 1418 (1977)
T.J. Rolfe, S.A. Rice, J. Dancz, J. Chem. Phys. 70, 26 (1979)
A.P. Chetverikov, W. Ebeling, M.G. Velarde, Int. J. Bifurcation Chaos 16, 1613 (2006)
J.C. Slater, Quantum Theory of Molecules and Solids, vol. 4 (McGraw-Hill, New York, 1974)
A.A. Voityuk, J. Jortner, M. Bixon, N. Rösch, Chem. Phys. Lett. 324, 430 (2000)
A.S. Davydov, Solitons in Molecular Systems, 2nd. edn. (Reidel, Dordrecht, 1991). (And references therein)
A.C. Scott, Phys. Rep. 217, 1 (1992)
P.L. Christiansen, A.C. Scott (Eds.), Davydov’s Soliton Revisited. Self-Trapping of Vibrational Energy in Protein (Plenum, New York, 1983)
P.S. Lomdahl, W.C. Kerr, Phys. Rev. Lett. 55, 1235 (1985)
L. Cruzeiro-Hansson, S. Takeno, Phys. Rev. E 56, 894 (1997). (And references therein)
D. Hennig, A.P. Chetverikov, M.G. Velarde, W. Ebeling, Phys. Rev. E 76, 046602 (2007)
M.G. Velarde, W. Ebeling, A.P. Chetverikov, D. Hennig, Int. J. Bifurcation Chaos 18, 521 (2008)
L.A. Cisneros-Ake, A.A. Minzoni, Phys. Rev. E 85, 021925 (2012)
M.G. Velarde, J. Comput. Appl. Math. 233, 1432 (2010)
A.V. Zolotaryuk, K.H.S. Spatschek, A.V. Savin, Europhys. Lett. 31, 531 (1995)
Yu.B. Gaididei, P.L. Christiansen, S.F. Mingaleev, Physica Scripta 51, 289 (1995)
A.V. Zolotaryuk, K.H.S. Spatschek, A.V. Savin, Phys. Rev. B 54, 266 (1996)
M.G. Velarde, W. Ebeling, A.P. Chetverikov, Int. J. Bifurcation Chaos 18, 3815 (2008)
E.M. Conwell, Proc. Natl. Acad. Sci. U.S.A. 102, 8795 (2005)
J.-H. Park, H.-Y. Choi, E.M. Conwell, J. Phys. Chem. B 108, 19483 (2004)
L.A. Cisneros, A.A. Minzoni, Stud. Appl. Math. 120, 333 (2008)
A.B. Aceves, L.A. Cisneros-Ake, A.A. Minzoni, Discret. Contin. Dyn. Syst. – Ser. S. 4, 975 (2011)
Acknowledgements
The authors acknowledge fruitful discussions with A.A. Alexandrov (deceased), L. Brizhik, A.P. Chetverikov, L. Cruzeiro, W. Ebeling, and D. Hennig. L.A.C.-A. gratefully acknowledges support from COFAA-IPN and project IPN-CGPI-20120651. M.G.V. acknowledges support from the Del Amo Foundation for a visit to the University of California at Irvine. This research has been supported in part by the Spanish Ministerio de Economía y Competitividad under Grant MAT2011-026221.
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Cisneros-Ake, L.A., Minzoni, A.A., Velarde, M.G. (2014). Variational Approximation to Electron Trapping by Soliton-Like Localized Excitations in One-Dimensional Anharmonic Lattices. In: Carretero-González, R., Cuevas-Maraver, J., Frantzeskakis, D., Karachalios, N., Kevrekidis, P., Palmero-Acebedo, F. (eds) Localized Excitations in Nonlinear Complex Systems. Nonlinear Systems and Complexity, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-02057-0_11
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