Extended projector method: Application to Jahn-Teller and pseudo-Jahn-Teller systems

Within the Trotter-Suzuki approximations on e^–βH, the extended projector method previously introduced by us is shown to be a valuable technique in investigating the general class of few-level systems coupled both linearly and quadratically to a selected number of harmonic oscillators. As an illustration we compare eigenvalues and Ham-reduction factors with the literature for the cubic linear Jahn-Teller systems Txε and Txτ2 as well as for the system Exε for which a quadratic warping interaction is included. For the latter system a symmetry projector is additionally developed, dealing with the transformation properties of nonlinear combinations of representational basis functions. As another illustration, the low-energy eigenstates of a two-level system quadratically coupled to a single harmonic oscillator are investigated. Within the ground state, the system becomes unstable at high coupling strengths and through the evaluation of time- and frequency-dependent correlation functions we found substantially different ground-state dynamic properties compared with those of a linearly coupled system.