Solitons, generalised master equations and small-polaron propagation

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Abstract
For an electron interacting with harmonic dispersive phonons in a periodic lattice, the possibility of wave (soliton)-like solutions of the generalised master equations (GME) for the electron site occupation probabilities is investigated. For the current form of the small-polaron Hamiltonian, the long-time asymptotics of the memory functions (kernels of the GME) in the small-polaron basis are discussed to all orders in the electron hopping integrals.Using this result, one obtains (for the initially localised electron) the t2-behaviour of the mean-square electron displacement at zero temperature. This corresponds to existing soliton solutions of the Schrodinger equation. At non-zero temperatures, the wave solution is damped.