Self-trapping in an asymmetric two-site Holstein model

We examine numerically the long-time average probability in a two-site system, for finding an electron staying at an initially occupied site for an asymmetric quantum Holstein electron-phonon coupled model. The principal finding is the existence of quantum-mechanical resonant tunnelling channels in the electron localization phenomenon. Based on a strong-coupling perturbative analysis, we have explained the presence of the channels as a consequence of a general resonant effect on an effective two-level system. Finally, a comparison of the quantum problem with the semiclassical description given by the Discrete Nonlinear Schrodinger equation is performed.