Bloch internal dynamics of a polaron uniformly moving in a constant electric field along molecular chains of various lengths

In this paper a close consideration is given to a uniform motion of a Holstein polaron in a constant electric field along a homogeneous polynucleotide chain, the parameters of which are close to those of a DNA chain. Earlier we showed that when a polaron moves uniformly along a chain, Bloch oscillations do not completely disappear. It was shown that with uniform motion of a polaron low-density components of the polaron arise with their own internal Bloch dynamics, different from the dynamics of the macro-part of the polaron. In this work we show how the character of distribution of a moving polaron depends on the values of the chain parameters and on the chain length. Consideration is given to peculiarities and difficulties of numerical modeling of this problem concerned with taking into account the structure of the polaron, uniformly moving in a constant electric field. It is shown that a polaron with a characteristic size of less than 10 sites and located thousands of sites from the end of a chain “feels” the end of the chain to which it moves. Such “sensitivity” is due to the presence of low-density components of the polaron during its movement in a constant electric field, and the polaron demonstrates this in the case when the low-density components of the polaron do not fit into a given chain.