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

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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.

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Authors and Affiliations

  1. Department of Theoretical Physics, Palacký University, Tř. 17. listopadu 50, 77207, Olomouc, Czech Republic

    E. Majerníková & S. Shpyrko

  2. Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta, 84 228, Bratislava, Slovak Republic

    E. Majerníková

  3. Institute of Mathematics, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovak Republic

    V. Majerník

Authors
  1. E. Majerníková
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  2. V. Majerník
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  3. S. Shpyrko
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Correspondence to E. Majerníková.

Additional information

Received: 22 September 2003, Published online: 20 April 2004

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

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Majerníková, E., Majerník, V. & Shpyrko, S. Entropic uncertainty measure for fluctuations in two-level electron-phonon models. Eur. Phys. J. B 38, 25–35 (2004). https://doi.org/10.1140/epjb/e2004-00095-y

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  • DOI: https://doi.org/10.1140/epjb/e2004-00095-y

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