Entropic uncertainty measure for fluctuations in two-level electron-phonon models

Abstract

Two-level electron-phonon systems with reflection symmetry linearly coupled to one or two phonon modes (exciton and E$\otimes (b_1+b_2)$ 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.

arXiv comment14 pages, 10 figs, published in Eur.Phys.J 38 B (2004) 25-35

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Cited by in corpus (2)

• Entropic uncertainty relations and topological-band insulator transitions in 2D gapped Dirac materials
• Level-dynamic approach to the excited spectra of the Jahn-Teller model - kink-train lattice and 'glassy' quantum phase