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

TL;DR

This paper introduces an entropic measure based on Shannon entropy to effectively describe quantum fluctuations in complex two-level electron-phonon systems, outperforming traditional variance-based measures.

Contribution

It demonstrates that Shannon entropies provide a proper global description of quantum fluctuations in two-level electron-phonon models, with numerical and variational analyses supporting this.

Findings

Shannon entropies effectively characterize quantum fluctuations.

Variance measures have limitations in describing fluctuations.

Numerical and variational methods validate the entropic approach.

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.