Numerical investigation of the dynamics of polaron states

A numerical scheme for solving a system of the nonlinear differential equations describing the evolution of the polaron in a homogeneous environment has been investigated. An accuracy of the computational scheme is analyzed. The obtained results allows us to conclude that if in an initial state the polaron was in a particular state (basic or excited one), it remains in this state irrespective of the presence or absence of damping in the system. It is shown that the initial charge distributions given by some superpositions at presence in the system of damping eventually evolve to a basic state. No evolution to a basic state is observed at the absence of damping in the system.