Polaron dynamics on the lattice with cubic nonlinearity. Accurate solution and multipeaked polarons

Background. The feasible mechanism of charge transfer in quasi-one-dimen­sional systems is examined. Special interest to this problem emerged after the experimental discovery that the charge can travel dozens nanometers through the DNA chain with very high efficiency. It was found additionally that the charge transfer probability weakly depends on the lattice length and, moreover, occurs as a single-step coherent process. These properties open the possibilities for the usage of these and analogous systems as nanosized electroactive devices. The primary goal of the present paper is the theoretical and numerical feasibility study of the charge transfer in one-dimensional systems, representing the simplified DNA model, by means of polarons. Materials and methods. The discrete model of one-dimensional classical oscillators with the cubic nonlinearity is utilized for the studying the problem, aimed at the elucidating the polaron mechanism of the charge transfer. The electron-phonon interaction is accounted in terms of the Su-Schriffer-Heeger (SSH) approximation. The referenced discrete model is reduced to two coupled nonlinear partial differential equations. One describes classical dynamical degrees of freedom. The other is the time-dependent Schrodinger equation for the electron wave function. The soliton-type solutions are derived at the definite relation between the model parameters (nonlinearity parameter $\alpha$ and the electron-phonon interaction $\chi$). The numerical modeling shows the very high stability (polarons travel thousandth lattice sites without substantial changes in shape and amplitude). New polaron types with the envelope consisting of few (from 2 to 5) peaks are found in numerical simulation at larger parameter values. These properties are manifested for supersonic polarons with large amplitudes. The peaks existence is explained by the fact that the dynamically polaron is comprised by few solitons held together by the electron-phonon interaction. Multipeaked polarons are also very stable. Results. The polaronic charge transfer mechanism is analyzed. The one-dimensional lattice model is used. The employed model describes the lattice dynamics classically. An accounting of the cubic nonlinearity in the neighboring particles interaction, allows to make the model more adequate with regard to original complex biological systems. Additionally, new qualitative properties are revealed. One is the existence of solitons and the role they are playing in the charge transfer. The wave function is reported in the adiabatic approximation, and the electron-phonon interaction is accounted in terms of the SSH approximation. Analytical solutions are derived for polarons on the nonlinear lattice. The solution shape (amplitude, width) is soliton-like and is governed by a single free parameter. Stable polarons with the envelope consisting of few peaks are found in numerical modelling. Conclusions. It has been established that polarons on the lattice with the cubic nonlinearity are very stable and can participate in the charge and energy transfer in DNA and polypeptides. New types of multypeaked polarons are found. The dynamics is interpreted as the coupled state of few solitons hold together by the ekectron-phonon interaction.