Quantum dynamics of the prototype polaron model

Citation
U. Herfort et M. Wagner, Quantum dynamics of the prototype polaron model, J PHYS-COND, 13(14), 2001, pp. 3297-3326
Citations number
32
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Apllied Physucs/Condensed Matter/Materiales Science
Journal title
JOURNAL OF PHYSICS-CONDENSED MATTER
ISSN journal
0953-8984 → ACNP
Volume
13
Issue
14
Year of publication
2001
Pages
3297 - 3326
Database
ISI
SICI code
0953-8984(20010409)13:14<3297:QDOTPP>2.0.ZU;2-L
Abstract
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.