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

TL;DR

This paper analytically investigates the phase-space features of Wigner flow in an anharmonic quantum system with a modified harmonic oscillator potential, proposing a method to quantify non-classicality through information fluxes.

Contribution

It introduces an analytical description of Wigner currents in an anharmonic system and links phase-space fluxes to measures of quantum non-classicality.

Findings

Wigner flow can be used to probe quantumness in anharmonic systems.

Quantum fluctuations are quantifiable via information fluxes in phase-space.

The approach applies broadly to anharmonic quantum systems driven by quantum wells.

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.