Polaron Dynamics on the Nonlinear Lattice in the Su-Schrieffer-Heeger Approximation. Exact and Approximate Solutions
T.Yu. Astakhova, V.A. Kashin, V.N. Likhachev and G.A. Vinogradov
Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Kosygina 4, Moscow 119991, Russian Federation
Received: April 9, 2015; In final form: October 19, 2015
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We investigate the polaron dynamics on the nonlinear lattice with the cubic nonlinearity in the tight-binding approximation. The electron-phonon interaction is accounted in the Su-Schrieffer-Heeger approximation. The system of nonlinear partial differential equations is derived in the continuum approximation. It has an exact solution at a special relation between parameters of lattice nonlinearity α and electron-phonon interaction χ. An approximate analytical solution is obtained at arbitrary parameters α and χ. Results of the numeric simulations are in a good agreement with the analytical predictions in both cases. The range of parameter values, where theoretical formulae are valid, is determined.

DOI: 10.12693/APhysPolA.129.334
PACS numbers: 71.38.-k, 72.10.Di