Polaron on a one-dimensional lattice: II. A moving polaron

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 − βx 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 β and parameter of electron-phonon interaction α). 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 α and β 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.

Polaron Dynamics on the Nonlinear Lattice in the Su-Schrieffer-Heeger Approximation. Exact and Approximate Solutions

“…Solution (9) has the form coinciding with the exact solution [26,28] for the harmonic lattice, i.e. when α = 0 in (8).…”

“…However, if the lattice is harmonic, i.e. α = 0 then the polaron velocity coincides with the polaron velocity on the harmonic lattice [26,28]. Thus, the expression for the polaron velocity (10) is correct in two limiting cases.…”

“…We compare the results on the anharmonic lattice with the exact solutions on the harmonic lattice [28]. Figure 1a shows the dependence of the unmovable polaron amplitude A on χ for both harmonic and anharmonic lattices.…”

“…Few examples are known where the exact or approximate solutions are derived. One is the polaron solution on the harmonic lattice in SSH approximation [26][27][28]. It has the hyperbolic secant form typical for soliton solution.…”

Polaron on harmonic lattice in electric field. Generation of coherent oscillations

“…For small EPI parameter (χ ≤ 0.4) the continuum approximation is valid and analytical relations 83 for relative displacements of neighbouring particles qj ≡ (xj -xj-1) and the wave function ψj(t) are available (eqn. 6), where A and D are amplitudes of relative particles displacements and wave function, respectively, 1/d is a polaron width, j0 is the initial polaron centre, v is the polaron velocity.…”