**Numerical Simulation of Small Radius Polaron in a Chain with Random Perturbations **
**Nadezhda S. Fialko, Victor D. Lakhno **
*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**. In a number of publications about biophysical experiments on the transfer of a charge to DNA, it is assumed that charge is transferred via a super-exchange mechanism at short distances of 2–3 nucleotide pairs, and in long fragments the charge forms a polaron that moves along the chain under the influence of temperature fluctuations. Using numerical simutation, we investigate the dynamics of a polaron of small radius in a homogeneous chain plaiced in constant electric field at a finite temperature. It is shown that there is no charge transfer by the polaron mechanism, i.e. there is no sequential movement of the polaron from site to site, in chains with parameter valuess corresponding to homogeneous adenine DNA fragments. The “polaron or delocalized state” check is based on the control of the average characteristics: the delocalization parameter, the position of the maximum probability, and the maximum modulus displacement. The dynamics of individual trajectories is also considered. Without electric field, there is a mode of switching between the states "stationary polaron – delocalized state", and a new polaron arises at a random site of the chain. In the chain placed in field with constant intensity, the averaged charge moves in the direction of the field, but the transfer occurs in a delocalized state.

**Key words**: *Holstein model, small radius polaron, Langevin equation, electric field intensity, * *DNA.*