Testing non-classicality with exact Wigner currents for an anharmonic quantum system

Abstract

Phase-space features of the Wigner flow for an anharmonic quantum system driven by the harmonic oscillator potential modified by the addition of an inverse square (one-dimension Coulomb-like) contribution are analytically described in terms of Wigner functions and Wigner currents. Reporting about three correlated continuity equations which quantify the flux of quantum information in the phase-space, the non-classicality profile of such an anharmonic system can be consistently obtained in terms of the fluxes of {\em probability}, {\em purity} and {\em von Neumann-like entropy}. Considering that quantum fluctuations can be identified from distortions over the classical regime, they can be quantified through the above-mentioned information fluxes whenever some {\em classically bounded} volume of the phase-space is selected. Our results suggest that the Wigner flow approach works as a probe of quantumness and classicality for a large set of anharmonic quantum systems driven by quantum wells.

20 pages, 03 figures

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• Wigner flow reveals topological order in quantum phase space dynamics
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• Wigner's representation of quantum mechanics in integral form and its applications
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