Quantum dynamics of the prototype polaron model

Abstract

The ab initio description of evolutionary processes in extendedelectron-phonon systems (polaronic transport, excitonic transfer,etc) up to the present is beyond numerical accessibility, since itrequires the simultaneous knowledge of all eigenfunctions andeigenvalues. Therefore, usually rough approximations are made, such as asemiclassical treatment.However, as we have shown in a recent paper, the full quantum-mechanicaltreatment drastically deviates from the semiclassical approximation (evenin a qualitative manner).In the concept discussed here unitary product transformations areintroduced, the constituents of which account for the two antagonistictendencies inherent in every coupled electron-phonon Hamiltonian. Weapply our procedure to the concrete case of the dimer-oscillator model by choosing foreach of the antagonistic tendencies respectively a one parameter unitaryoperator, such that full analytical diagonalization is reached in theopposing limits of the Hamiltonian constituents. In the intermediate regimethe two parameters of the transformation are suitably optimized. In thismanner the generation of the full spectrum of eigensolutions involves twoanalytically fixed parameters only. The evolutionary behaviour resultingfrom our procedure is contrasted with the exact numerical result as well aswith 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 asatisfactory manner in all intrinsic physical parameter regimes (couplingand transfer) and overcomes the drastic shortcomings of previouscalculations.