Institute of Mathematical Problems of Biology RAS - the Branch of Keldysh Institute of Applied Mathematics of Russian Academy of Sciences,  Pushchino, Moscow Region, Russia

Abstract. A study of the nature of the motion of a Holstein polaron in a homogeneous polynucleotide chain in a constant electric field, depending on the initial polaron state, was carried out. The calculations performed showed that the duration of the uniform motion of the polaron along the chain is finite and depends on the entire set of system parameters, including the characteristic size of the initial polaron state. It is shown that at a fixed value of the electric field intensity, an increase in the characteristic size of the initial polaron state leads to a decrease in the time of uniform motion of the polaron along the chain. The calculations carried out earlier showed that with the uniform movement of the polaron along the chain, low-density components of the polaron are formed immediately after the electric field is turned on. Moreover, the low-density components of the polaron have their own internal dynamics, which are different from the dynamics of the macro-part of the polaron. With uniform motion, the macro-part of the polaron moves at a constant velocity, maintaining its shape, while the low-density components of the polaron demonstrate such characteristics of Bloch oscillations as the period of Bloch oscillations and the maximum Bloch amplitude. It is also shown that a change in the shape of the initial polaron state exerts influence upon not only the duration of the uniform motion of the polaron along the chain, but also the characteristics of the low-density components of the polaron.

Key words: nanobioelectronics, nanowire, molecular chain, polaron, DNA, charge transfer, Holstein model.