https://doi.org/10.1140/epjb/e2004-00095-y
Entropic uncertainty measure for fluctuations in two-level electron-phonon models
1
Department of Theoretical Physics, Palacký University, Tř. 17. listopadu 50, 77207 Olomouc, Czech Republic
2
Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta, 84 228 Bratislava, Slovak Republic
3
Institute of Mathematics, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovak Republic
Corresponding author: a majere@prfnw.upol.cz
Received:
22
September
2003
Published online:
20
April
2004
Two-level electron-phonon systems with reflection symmetry
linearly coupled to one or two phonon modes
(exciton and E
Jahn-Teller model)
exhibit strong enhancement of quantum fluctuations
of the phonon coordinates and momenta
due to the complex interplay of quantum fluctuations and nonlinearities
inherent to the models.
We show that for the complex correlated quantum fluctuations of the
anisotropic two-level systems the Shannon entropies of phonon
coordinate and momentum and their sum yield their proper global description.
On the other hand, the variance measures of the
Heisenberg uncertainties suffer from several shortcomings to provide proper
description of the fluctuations.
Wave functions, related entropies and variances
were determined by direct numerical simulations.
Illustrative variational calculations were performed to demonstrate
the effect on an analytically tractable exciton model.
PACS: 71.38.-k – Polarons and electron-phonon interactions / 63.70.+h – Statistical mechanics of lattice vibrations and displacive phase transitions / 02.50.-r – Probability theory, stochastic processes and statistics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004
