Quantum dynamics of the prototype polaron model

The ab initio description of evolutionary processes in extended electron-phonon systems (polaronic transport, excitonic transfer, etc) up to the present is beyond numerical accessibility, since it requires the simultaneous knowledge of all eigenfunctions and eigenvalues. Therefore, usually rough approximations are made, such as a semiclassical treatment. However, as we have shown in a recent paper, the full quantum-mechanical treatment drastically deviates from the semiclassical approximation (even in a qualitative manner). In the concept discussed here unitary product transformations are introduced, the constituents of which account for the two antagonistic tendencies inherent 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 limits of the Hamiltonian constituents. In the intermediate regime the two parameters of the transformation are suitably optimized. In this manner the generation of the full spectrum of eigensolutions involves two analytically fixed 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') unitary transformation frequently used in the literature. It is shown that our calculation approaches the exact result in a satisfactory manner in all intrinsic physical parameter regimes (coupling and transfer) and overcomes the drastic shortcomings of previous calculations.