  We investigate the scattering of an electron by phonons in a small structure
between two one-dimensional tight-binding leads. This model mimics the quantum
electron transport through atomic wires or molecular junctions coupled to
metallic leads. The electron-phonon coupled structure is represented by the
Holstein model. We observe permanent energy transfer from the electron to the
phonon system (dissipation), transient self-trapping of the electron in the
electron-phonon coupled structure (due to polaron formation and multiple
reflections at the structure edges), and transmission resonances that depend
strongly on the strength of the electron-phonon coupling and the adiabaticity
ratio. A recently developed TEBD algorithm, optimized for bosonic degrees of
freedom, is used to simulate the quantum dynamics of a wave packet launched
against the electron-phonon coupled structure. Exact results are calculated for
a single electron-phonon site using scattering theory and analytical
approximations are obtained for limiting cases.
