Phonon operators

The electron-phonon operator is a tensor product between the electronic dipole and the nuclear dipole operators. A mixing between the AA and BB via the singlet-spin diradical AB state is possible now. A linear superposition of identical vibration states in AA and BB is performed by the excited state diradical AB. If the system started at cis state, after coupling may decohere by emission of a vibration photon in the trans state furthermore, relaxation to the trans... 

For what follows it is essential that equation (3) for the large-time asymptotic of the phonon correlation function holds rather generally, including cases if the interaction Hamiltonian contains more than two phonon operators and the Hamiltonian cannot be diagonalized [13,14]. This allows one to apply the method for the description of multiphononon relaxation processes caused by higher order anharmonicities. 

In terms of the creation-annihilation electron and phonon operators the Hamiltonian can be cast as follows ... 

On the assumption of bimolecular interactions of rigid molecules, Denm depends only on the translational and rotational degrees of freedom of molecules n and m. Let xj, be the six coordinates of molecule a in unit cell n. Using (2.9) with appropriate coefficients eq s, // may be expressed in terms of phonon operators ... 

Kanamori in his seminal work [3] suggested a more general approach called the displacement operator method. According to this method the initial bk phonon operators are replaced in the Hamiltonian (1) with the ak new ones like that... 

The system-reservoir interaction operators are products of the type Vak = AR, where A represents a molecule operator (aj, a, B, B) and R a reservoir operator b, b ). Because of the BO approximation the electronic operators commute with the phonon operators. Moreover, the pseudolocalized phonon operators commute with those of the baind phonons because of the boson commutation rules. This amounts to the statement that all molecule variables commute with the reservoir variables, [A,R] = 0. 

It is clear that the standard molecular approach and the Q C model are correlated in the sense that their corresponding Hamiltonians are isometric. However, within the Q C model, the handling of the separation between electrons and nuclei is conceptually different. In the latter, the electrons and a PCB subsystem endowed with mass are coupled via electron-phonon operators usually employed for descrihing Jahn-Teller effects... 

An effective Hamiltonian of file electron subsystem can be constructed with the displaced phonon operator method (Elliott et al. 1972, Young 1975) or the method of canonical transformation (Mutscheller and Wagner 1986) analoguous results are given by a perturbation method in the second order in the electron-qrhonon interaction (13) (Baker 1971). 

Vf, V = first and second order contributions in the phonon operators of the magneto-elastic interactions = electrostatic potential = components of the deformation tensor... 

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