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We investigate a quasi-particle coupled to polarization vibrations in a dimer model. This model (harmonic oscillator coupled to a two-level system) is interesting for various physical situations, e.g. the transport of excitons in dimers or the spin- 1 2 case of the Jaynes-Cummings model. We found that a complementary approach to the usual quasi-classical treatment of the spin-boson model may be more...