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

摘要

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 alpha and electron-phonon interaction chi. An approximate analytical solution is obtained at arbitrary parameters alpha and chi. 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.