On the dynamics of polaron formation in a deformable medium

We consider the standard model for exciton transport in which the energy of interaction between the exciton and the lattice is linear in the lattice coordinates and local in the exciton coordinates. We focus on the dynamics of polaron formation by restricting our analysis to the immobile exciton limit in which the model is exactly solvable. We study the evolution of the many-body system from initial states representing a bare exciton in a quiescent bare lattice and a polaron in a quiescent dressed lattice. The total energy, the dynamical energy content of the bare lattice, the deformation of the bare lattice, and many-body Green’s functions are calculated exactly. The reduced density matrix appropriate to each initial condition is obtained exactly for any temperature.