Geodesic
Two types of oscillations of the Holstein polaron uniformly moving along a polynucleotide chain in a constant electric field
Matematičeskaâ biologiâ i bioinformatika, Tome 14 (2019) no. 2, pp. 477-487.

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In connection with the development of molecular nanobioelectronics, the main task of which is the construction of electronic devices based on biological molecules, the problems of charge transfer in such extended molecules as DNA are of increasing interest. The relevance of studying the charges motion in one-dimensional molecular chains is primarily associated with the possibility of using these chains as wires in nanoelectronic devices. Current carriers in one-dimensional chains are self-trapped electronic states, which have the form of polaron formations. In this paper we investigate the motion of the Holstein polaron in the process of its uniform motion along the chain in a constant electric field. It is known that during uniform motion along the chain in a weak electric field, the polaron experiences small oscillations of its shape. These oscillations are associated with the discreteness of the chain and are due to the presence of the Peierls–Nabarro potential in the discrete chain. Previous investigations have shown that for certain parameters of the chain, there is the possibility of uniform charge motion in a constant electric field over very large distances. The charge motion with a constant velocity is possible for small values of the electric field intensity. With an increase in the electric field intensity, the charge goes into an oscillatory regime of motion with Bloch oscillations. The calculations performed in this work showed that the elements of Bloch oscillations also appear during stationary motion of the polaron along the chain. Thus, it is shown that the Holstein polaron, uniformly moving along the chain in a constant electric field, experiences not only Peierls–Nabarro oscillations, but also low-amplitude oscillations with a Bloch period. 
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A. N. Korshounova; V. D. Lakhno. Two types of oscillations of the Holstein polaron uniformly moving along a polynucleotide chain in a constant electric field. Matematičeskaâ biologiâ i bioinformatika, Tome 14 (2019) no. 2, pp. 477-487. http://geodesic.mathdoc.fr/item/MBB_2019_14_2_a13/

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