Geodesic
Polarons on dimerized lattice of polyacetilene. Continuum approximation
Matematičeskaâ biologiâ i bioinformatika, Tome 16 (2021), pp. 335-348.

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A one-electron model is proposed to describe a polaron on a dimerized polyacetylene lattice. Within the framework of the formulated model, the dynamics of a freely moving polaron is considered. The results obtained are compared with the many-electron model that takes into account all $\pi$-electrons of the valence band. Polaron can move at subsonic and supersonic speeds. The subsonic polaron is stable. A supersonic polaron loses stability at times $\sim$ 6000 fs. A supersonic polaron has a forbidden speed range. An analytical solution to the continual approximation helps to understand the reason for the existence of forbidden speeds. The dynamics of a free polaron is similar to the dynamics of a polaron in an electric field. The proposed one-electron approximation significantly expands the possibilities of numerical simulation in comparison with the traditional many-electron model. 
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T. Yu. Astakhova; G. A. Vinogradov. Polarons on dimerized lattice of polyacetilene. Continuum approximation. Matematičeskaâ biologiâ i bioinformatika, Tome 16 (2021), pp. 335-348. http://geodesic.mathdoc.fr/item/MBB_2021_16_a6/

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