Polarons on the One-Dimensional Lattice in the Su–Schrieffer–Heeger Model. Charge Transfer in DNA

Polarons on the one-dimensional lattice are thoroughly analyzed. A lattice consists of particles interacting via the nearest-neighbor potential — harmonic or nonlinear. The electron-phonon interaction is accounted in the Su–Shrieffer–Heeger approximation. Initially the unmovable polarons on the harmonic lattice are considered. Analytical expressions for both small and large radii polarons are derived. Solutions for the movable polarons are obtained in the continuous approximation. Their stability is verified in numerical simulation. Exactly integrable equations are also derived with multisoliton solutions. Analytical solutions are obtained for the anharmonic lattice with the potential $U(q)=q_2/2-\beta q_3/3$. Analytical solutions are obtained in the continuum approximation. Stable solutions also exist in the range of parameters where the continuum approximation is invalid. Polarobreathers with the envelope consisting of few peaks are found. The polaron velocity is determined by the concurrence of lattice nonlinearity $\beta$ and the electron-phonon interaction and can exceed the sound velocity. Few particular cases of the polaron evolution on the finite length lattice are considered. An applicability of the considered model to the charge transfer in DNA is briefly analyzed.