Finite-temperature two-state small-polaron dynamics: Averaged Hamiltonian approach

We study small-polaron self-trapping properties in the two-state molecular crystal model by employing a finite-temperature variational non-adiabatic approach that is an extension to the semiclassical adiabatic Pekar theory. We find two distinct regions in the space of coupling constant versus adiabaticity parameter that are separated by a temperature-dependent critical line. In these regions the response of the lattice to the motion of the particle is quite different. We find conditions that allow for the determination of the character of the motion and the localization transition as a function of the physical parameters of the system and temperature.