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Mat. Biolog. Bioinform., 2010, Volume 5, Issue 1, Pages 1–29 (Mi mbb48)  

This article is cited in 8 scientific papers (total in 8 papers)

Mathematical Modeling

Formation of stationary electronic states in finite homogeneous molecular chains

V. D. Lakhno, A. N. Korshounova

Institute of Mathematical Problems of Biology, Russian Academy of Sciences

Abstract: 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.

Key words: DNA, nanoelectronics, quantum, dissipative, numerical, hyperbolic, relaxation, solitons, multisolitons.

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UDC: 577, 51-7
Received 05.02.2010, Published 30.04.2010

Citation: V. D. Lakhno, A. N. Korshounova, “Formation of stationary electronic states in finite homogeneous molecular chains”, Mat. Biolog. Bioinform., 5:1 (2010), 1–29

Citation in format AMSBIB
\by V.~D.~Lakhno, A.~N.~Korshounova
\paper Formation of stationary electronic states in finite homogeneous molecular chains
\jour Mat. Biolog. Bioinform.
\yr 2010
\vol 5
\issue 1
\pages 1--29

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    This publication is cited in the following articles:
    1. Li G., Movaghar B., Ratner M.A., “Dynamic Electron Localization Initiated by Particle-Bath Coupling”, Phys. Rev. B, 87:9 (2013), 094302  crossref  adsnasa  isi  elib  scopus
    2. V. D. Lakhno, N. S. Fialko, “Usloviya suschestvovaniya polyaronnykh sostoyanii v klassicheskikh molekulyarnykh tsepochkakh pri konechnykh temperaturakh”, Matem. biologiya i bioinform., 9:1 (2014), 1–3  mathnet
    3. Lakhno V.D., “Large-Radius Holstein Polaron and the Problem of Spontaneous Symmetry Breaking”, Prog. Theor. Exp. Phys., 2014, no. 7, 073I01  crossref  zmath  isi  elib  scopus
    4. Korshunova A.N., Lakhno V.D., “a New Type of Localized Fast Moving Electronic Excitations in Molecular Chains”, Physica E, 60 (2014), 206–209  crossref  isi  elib  scopus
    5. A. N. Korshunova, V. D. Lakhno, “Osobennosti dvizheniya polyarona v molekulyarnykh polinukleotidnykh tsepochkakh konechnoi dliny”, Matem. biologiya i bioinform., 11:2 (2016), 141–158  mathnet  crossref
    6. A. N. Korshunova, V. D. Lakhno, “Bystroe formirovanie dvizhuschegosya polyaronnogo sostoyaniya v odnorodnoi molekulyarnoi polinukleotidnoi tsepochke konechnoi dliny”, Preprinty IPM im. M. V. Keldysha, 2018, 231, 22 pp.  mathnet  crossref  elib
    7. Korshunova A.N., Lakhno V.D., “Simulation of the Stationary and Nonstationary Charge Transfer Conditions in a Uniform Holstein Chain Placed in Constant Electric Field”, Tech. Phys., 63:9 (2018), 1270–1276  crossref  isi  scopus
    8. A. N. Korshunova, V. D. Lakhno, “Osobennosti dvizheniya zaryada v odnorodnykh molekulyarnykh polinukleotidnykh tsepochkakh konechnoi dliny. Bystroe formirovanie dvizhuschegosya polyaronnogo sostoyaniya”, Matem. biologiya i bioinform., 13:2 (2018), 534–550  mathnet  crossref
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