Polarons on one-dimensional lattice. II. Moving polaron

TL;DR

This paper investigates moving polarons in one-dimensional lattices, deriving PDE models with soliton solutions, exploring their dynamics, and relating findings to charge transfer in biomolecules like DNA.

Contribution

It introduces a continuum PDE framework for moving polarons on harmonic and inharmonic lattices, revealing new soliton solutions and dynamic behaviors including supersonic and multi-peak polarons.

Findings

Moving polarons described by soliton solutions with velocity up to sound speed.

Existence of supersonic polarons in inharmonic lattices.

Discovery of stable multi-peak polarobreather solutions.

Abstract

In the present study we revise the possible polaron contribution to the charge and energy transfer over long distances in biomolecules like DNA. The harmonic and the simple inharmonic ($U(x) = x^2/2 - \beta x^3/3$) lattices are considered. The systems of PDEs are derived in the continuum approximation. The PDEs have the one-soliton solution for polarons on the harmonic lattice. It describes a moving polaron, the polaron velocity lies in the region from zero to the sound velocity and depends on the polaron amplitude. The PDEs describing polarons on the inharmonic lattice also have the one-soliton solution only in the case of special relation between parameters (parameter of inharmonicity $\beta$ and parameter of electron-phonon interaction $\alpha$). Polaron dynamics is numerically investigated in the wide range of parameters, where the analytical solutions are not available. Supersonic polarons are observed on inharmonic lattice with high inharmonicity. There is the range of parameters $\alpha$ and $\beta$ where exists a family of unusual stable moving polarons with the envelope consisting of several peaks (polarobreather solution). The results are in qualitative agreement with recent experiments on the charge transport in DNA.