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JOURNALS // Matematicheskaya Biologiya i Bioinformatika // Archive

Mat. Biolog. Bioinform., 2021 Volume 16, Issue 1, Pages 152–168 (Mi mbb463)

Mathematical Modeling

Equilibrium charge distribution in a finite chain with a trapping site

N. S. Fialko, M. M. Olshevets, V. D. Lakhno

Institute of Mathematical Problems of Biology RAS – Branch of KIAM RAS, Pushchino, Russia

Abstract: The paper considers the problem of the distribution of a quantum particle in a classical one-dimensional lattice with a potential well. The cases of a rigid chain, a Holstein polaron model, and a polaron in a chain with temperature are investigated by direct modeling at fixed parameters. As is known, in the one-dimensional case, a particle is captured by an arbitrarily shallow potential well with an increase of the box size. In the case of a finite chain and finite temperatures, we have quite the opposite result, when a particle, being captured in a well in a short chain, turns into delocalized state with an increase in the chain length. These results may be helpful for further understanding of charge transfer in DNA, where oxoguanine can be considered as a potential well in the case of hole transfer when for excess electron transfer it is thymine dimer.

Key words: charge, potential well, Holstein model, Langevin equation, thermodynamic equilibrium state.

Received 01.04.2021, 24.05.2021, Published 06.06.2021

DOI: 10.17537/2021.16.152



© Steklov Math. Inst. of RAS, 2024