Ground state of the local model

Now we consider the same Hamiltonian, but taken for the local molecule (T = 0). From the outset we include the additional variational mixing parameter A into the Ansatz. The understanding of the importance of introducing the mixing parameter in the local model in the contrast to the lattice one can be gained if one examines the expressions for Hamiltonians, in particular, those terms, which contain the mixing of two phonon modes. The mixing is contained mostly in the local term with /3, 

The variational mean value of the part of the Hamiltonian (6) in the state (9) renormalized by Q yields (Appendix A) 

From equation (28) one can see that A causes correlations of the selftrapping and tunneling dominated regions. 

The ground states of equations (27), (29) and (31) were found by minimalization of the expressions against the involved VPs. The respective ground state energies /iopl, a=0 E°n=o anc T -o.A-o.opi will be compared mutually and with the exact value from numerical simulation in order to find out importance of the VPs 17, A in different regions of model parameters y= (/3/a) (reflection) and fL = (a2/fl2) (effective e-ph coupling). The place of E(f)e JT model will clearly come out as an important special case. 

Electron in the selftrapping dominated region is trapped by the phonons-1 but due to the interactions mediated by phonons-2 the electron can fluctuate to the higher level. Due to the reflection symmetry of the phonons-2 continuum oscillations of the electrons at simultaneous emission and absorption of phonons-1 occurs. These oscillations couple the levels and so the electrons into pairs. This mechanism was described in a recent paper [10] for a lattice model. 

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