Absorption line shape of a dynamical Jahn-Teller Center. Strong-interaction limit

The dynamic Jahn-Teller effect, induced in a localized center by light absorption and due to a singlet-multiplet electronic transition, is studied in the strong-interaction limit (SIL) of the electron-phonon interaction. The absorption line shape $R\left(\omega \right)$ is examined in the framework of the linear-response theory and the role of the host crystal in fading the correlations among the phonons associated to the electronic excitation is taken into account. $R\left(\omega \right)$ is deduced by using the Feynman-paths method and the most significant contribution from each path, when working in the SIL, is identified. It is shown that the so-called semiclassical model (SCM) corresponds to considering only the Markovian many-phonon processes in the motion of the crystal phonons coupled to the Jahn-Teller excited electron. It is also shown why a refined version of the SCM leads to an effective Hamiltonian, where the adiabatic potential energy is related only to a few interaction modes and effective frequencies. In particular, the interaction modes are found to be stochastic, and not dynamical, variables. A correction to the well-known SCM Toyozawa-Inoue expression is found and discussed. Finally, the phonon quantum effects on $R\left(\omega \right)$ in the SIL and beyond the SCM are introduced and commented on.