The ah initio description of evolutionary processes in extended electron-ph
onon systems (polaronic transport, excitonic transfer, etc) up to the prese
nt is beyond numerical accessibility, since it requires the simultaneous kn
owledge of all eigenfunctions and eigenvalues. Therefore, usually rough app
roximations are made, such as a semiclassical treatment. However, as we hav
e shown in a recent paper, the full quantum-mechanical treatment drasticall
y deviates from the semiclassical approximation (even in a qualitative mann
er).
In the concept discussed here unitary product transformations are introduce
d, the constituents of which account for the two antagonistic tendencies in
herent in every coupled electron-phonon Hamiltonian. We apply our procedure
to the concrete case of the dimer-oscillator model by choosing for each of
the antagonistic tendencies respectively a one parameter unitary operator,
such that full analytical diagonalization is reached in the opposing limit
s of the Hamiltonian constituents. In the intermediate regime the two param
eters of the transformation are suitably optimized. In this manner the gene
ration of the full spectrum of eigensolutions involves two analytically fix
ed parameters only. The evolutionary behaviour resulting from our procedure
is contrasted with the exact numerical result as well as with the one from
the semiclassical approach and also with a more simple ('displacive') unit
ary transformation frequently used in the literature.
It is shown that our calculation approaches the exact result in a satisfact
ory manner in all intrinsic physical parameter regimes (coupling and transf
er) and overcomes the drastic shortcomings of previous calculations.