Classical and statistical limits of the quantum singular oscillator

Autor(es)

Fernando e Silva, Caio ^[1] ; Bernardini, Alex E. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Fis, POB 676, BR-13565905 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 558, NOV 15 2020.
• Citações Web of Science: 0

Resumo

The classical boundaries of the quantum singular oscillator (SO) are addressed under Weyl-Wigner phase-space and Bohmian mechanics frameworks as to comparatively evaluate phase-space and configuration space quantum trajectories as well as to compute distorting quantum fluctuations. For an engendered pure state quasi-gaussian Wigner function that recovers the classical time evolution (at phase and configuration spaces), Bohmian trajectories are analytically obtained as to show how the SO energy and anharmonicity parameters drive the quantum regime through the so-called quantum force, which quantitatively distorts the recovered classical behavior. Extending the discussion of classical-quantum limits to a quantum statistical ensemble, the thermalized Wigner function and the corresponding Wigner currents are computed as to show how the temperature dependence affects the local quantum fluctuations. Considering that the level of quantum mixing is quantified by the quantum purity, the loss of information is quantified in terms of the temperature effects. Despite having contrasting phase-space flow profiles, two inequivalent quantum systems, namely the singular and the harmonic oscillators, besides reproducing stable classical limits, are shown to be statistically equivalent at thermal equilibrium, a fact that raises the SO non-linear system to a very particular category of quantum systems. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 18/03960-9 - Estruturas fundamentais da Mecânica Quântica no espaço de fases -- Não-classicalidade e correspondência clássico-quântica em sistemas quânticos ordinários e sistemas tipo-Dirac
• Beneficiário: Alex Eduardo de Bernardini
• Modalidade de apoio: Auxílio à Pesquisa - Regular