Non-classicality from the phase-space flow analysis of the Weyl-Wigner quantum mechanics

Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto - Rua do Campo Alegre, 4169-007, Porto, Portugal

^{(a) (b)} On leave of absence from Departamento de Física, Universidade Federal de São Carlos - PO Box 676, 13565-905, São Carlos, SP, BrazilAlso at Centro de Física do Porto - Rua do Campo Alegre, 4169-007, Porto, Portugal; alexeb@ufscar.br
^{(a) (b)} On leave of absence from Departamento de Física, Universidade Federal de São Carlos - PO Box 676, 13565-905, São Carlos, SP, BrazilAlso at Centro de Física do Porto - Rua do Campo Alegre, 4169-007, Porto, Portugal; orfeu.bertolami@fc.up.pt

Received: 30 October 2017
Accepted: 7 December 2017

Abstract

A fluid analog of the information flux in the phase-space associated to purity and von Neumann entropy is identified in the Weyl-Wigner formalism of quantum mechanics. Once constrained by symmetry and positiveness, the encountered continuity equations provide novel quantifiers for non-classicality (non-Liouvillian fluidity) given in terms of quantum decoherence, purity and von Neumann entropy fluxes. Through definitions in the Weyl-Wigner formalism, one can identify the quantum fluctuations that distort the classical-quantum coincidence regime, and the corresponding quantum information profile, whenever some bounded x − p volume of the phase-space is specified. The dynamics of anharmonic systems is investigated in order to illustrate such a novel paradigm for describing quantumness and classicality through the flux of quantum information in the phase-space.