Davydov's Solitons in a Homogeneous Nucleotide Chain

TL;DR

This paper models charge transfer via Davydov solitons in nucleotide chains using the Holstein Hamiltonian, analyzing how soliton path length depends on velocity, dispersion, and dissipation, and calculating their mobility and equilibrium velocity.

Contribution

It introduces a detailed analysis of Davydov soliton dynamics in nucleotide chains, including effects of dispersion and dissipation on soliton path length and mobility, which was not previously explored.

Findings

Soliton path length grows exponentially as velocity decreases in dispersionless case.

Presence of dispersion leads to infinite path length for velocities below V_0.

Dissipation results in finite soliton path length and defines an equilibrium velocity.

Abstract

Charge transfer in homogeneous nucleotide chains is modeled on the basis of Holstein Hamiltonian. The path length of Davydov solitons in these chains is being studied. It is shown that in a dispersionless case, when the soliton velocity V is small, the path length grows exponentially as V decreases. In this case the state of a moving soliton is quasisteady. In the presence of dispersion determined by the dependence $\Omega^2 = \Omega_0^2 + V_0^2\kappa^2$ \, the path length in the region 0 < V < V_0 is equal to infinity. In this case the phonon environment follows the charge motion. In the region V > V_0 the soliton motion is accompanied by emission of phonons which leads to a finite path length of a soliton. The latter tends to infinity as $V \rightarrow V_0 + 0$ and $V \rightarrow \infty$. The presence of dissipation leads to a finite soliton path length. An equilibrium velocity of soliton in an external electric field is calculated. It is shown that there is a maximum intensity of an electric field at which a steady motion of a soliton is possible. The soliton mobility is calculated for the stable or ohmic brunch.