TIME-DEPENDENT MEAN-FIELD THEORY FOR TUNNELING IN ELECTRON-PHONON SYSTEMS

A semiclassical method is presented for tunneling of self-trapped stat es in many-body systems with electrons and phonons. An overcomplete se t of Slater determinants, lattice coordinates, and lattice momenta is used to represent a functional integral. Stationary phase equations ar e solved numerically without any constraint on the dynamics of electro ns and phonons, i.e., without the use of the adiabatic approximation. To evaluate transition amplitudes, we integrate over small fluctuation s in both electronic and phonon degrees of freedom, keeping their time order correctly. This method can be applied to general electron-phono n systems and is useful when self-trapped states have complex structur es in charge or spin densities and lattice displacements. The effectiv e hopping strength is calculated for a self-trapped kink in the commen surate charge-density-wave state in one dimension. At strong coupling in the Holstein and attractive Hubbard models, where tunneling involve s effectively a single tightly bound bipolaron, this method reproduces previous analytic results. New results are obtained at intermediate c oupling where the kink is extended over a couple of lattice sites and for models with both electron-electron and electron-phonon interaction s.