Abstract
We study spontaneously localized electron states in a D-dimensional lattice with a nonlocal electron-phonon interaction. We show that, in the adiabatic long-wave approximation, such electron states are described by a modified nonlinear Schr\"odinger equation with a nonlocal nonlinear interaction which, within certain ranges of the parameter values, admits localized soliton-type solutions. We also calculate nonadiabatic corrections and estimate conditions of the applicability of the adiabatic approximation in one- and two-dimensional cases. We show that the adiabatic approximation is valid at strong enough electron-phonon coupling.
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