Fundamental structures of phase space quantum mechanics - Nonclassicality and classical-quantum correspondence applied to ordinary quantum mechanics and Dirac-like systems

• Grant number: 18/03960-9
• Support Opportunities: Regular Research Grants
• Start date: July 01, 2018
• End date: June 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Alex Eduardo de Bernardini
• Grantee: Alex Eduardo de Bernardini
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

This project is compartmentalized into two closely connected stages.The first stage contemplates the development and the use of new fundamental structures of quantum mechanics described according to Wigner's representation in phase space as to qualitatively and quantitatively describe the content of decoherence, non-classicality, locality and even continuous variable correlations of two quantum modes of ordinary quantum systems, in such a way as to test some recently introduced theoretical tools which quantify the classical-quantum correspondence for these systems.The second step involves the application of these tools to the dynamics described by the Dirac equation driven by the simplest classes of quantum potentials described according to the Poicar\'e's group classification.As a subsequent proposal, the details involving the preservation of covariant structures (symplectic, Lorentz, etc.) will be addressed in obtaining quantum correlations as entanglement of formation, geometric discord and logarithmic negativity.In particular, we expect that the inclusion of localization characteristics in Dirac-like systems, and the subsequent description of their influence on the quantum information content of these systems, can be described in Dirac-type platforms, from from trapped ions described according to the Jaynes-Cummings dynamics to graphene in double layers, which have been broadly framed in a description of Quantum Mechanics that we have developed in previous projects. (AU)

Scientific publications

(17)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BERNARDINI, A. E.; DA ROCHA, R.. Informational entropic Regge trajectories of meson families in AdS/QCD. Physical Review D, v. 98, n. 12, DEC 20 2018. (18/03960-9, 17/18897-8)

BERNARDINI, A. E.; DA ROCHA, R.. Phase-space quantum profile of Poschl-Teller two-level systems. EUROPEAN PHYSICAL JOURNAL PLUS, v. 134, n. 1, JAN 17 2019. (18/03960-9, 17/18897-8)

BERNARDINI, ALEX E.. Phase-space elementary information content of confined Dirac spinors. EUROPEAN PHYSICAL JOURNAL PLUS, v. 135, n. 8, AUG 25 2020. (18/03960-9)

BITTENCOURT, V. A. S. V.; BERNARDINI, A. E.; BLASONE, M.. Chiral oscillations. EPL, v. 139, n. 4, p. 7-pg., 2022-08-01. (18/03960-9)

BERNARDINI, ALEX E.; FERNANDO E SILVA, CAIO; IOP PUBLISHING. Anharmonic effects on phase-space quantum profiles: an exact approach. WAKE CONFERENCE 2021, v. 1612, p. 14-pg., 2020-01-01. (18/03960-9)

BERNARDINI, ALEX E.. Testing nonclassicality with exact Wigner currents for an anharmonic quantum system. PHYSICAL REVIEW A, v. 98, n. 5, p. 11-pg., 2018-11-26. (18/03960-9)

BERNARDINI, A. E.; DA ROCHA, R.. Informational entropic Regge trajectories of meson families in AdS/QCD. PHYSICAL REVIEW D, v. 98, n. 12, p. 10-pg., 2018-12-20. (18/03960-9, 17/18897-8)

BERNARDINI, ALEX E.. Testing nonclassicality with exact Wigner currents for an anharmonic quantum system. Physical Review A, v. 98, n. 5, NOV 26 2018. (18/03960-9)

BLASONE, MASSIMO; BITTENCOURT, VICTOR A. S. V.; BERNARDINI, ALEX E.. Helicity rotation induced by Lorentz boosts. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, v. 17, n. 8, SI, DEC 2019. (18/03960-9)

GAUY, HENRIQUE MATHEUS; BERNARDINI, ALEX E.. 5+1)-dimensional analytical braneworld models: Intersecting thick brane. PHYSICAL REVIEW A, v. 105, n. 2, JAN 25 2022. (18/03960-9)

BERNARDINI, ALEX E.; BERTOLAMI, ORFEU; ELZE, HT; BLASONE, M; DIOSI, L; FRONZONI, L; HALLIWELL, JJ; KIEFER, C; PRATI, E; VITIELLO, G. Phase-space continuity equations for quantum decoherence, purity, von Neumann and Renyi entropies. WAKE CONFERENCE 2021, v. 1275, p. 7-pg., 2019-01-01. (18/03960-9)

BLASONE, MASSIMO; BITTENCOURT, VICTOR A. S. V.; BERNARDINI, ALEX E.. Helicity rotation induced by Lorentz boosts. INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, v. 17, n. 8, p. 12-pg., 2019-12-01. (18/03960-9)

BERNARDINI, ALEX E.. On the elementary information content of thermodynamic ensembles. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 557, NOV 1 2020. (18/03960-9)

FERNANDO E SILVA, CAIO; BERNARDINI, ALEX E.. Classical and statistical limits of the quantum singular oscillator. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, v. 558, NOV 15 2020. (18/03960-9)

BERNARDINI, A. E.; DA ROCHA, R.. Cosmological comoving behavior of the configurational entropy. Physics Letters B, v. 796, p. 107-111, SEP 10 2019. (18/03960-9, 17/18897-8)

BERNARDINI, A. E.; BITTENCOURT, V. A. S. V.; BLASONE, M.. CP symmetry and thermal effects on Dirac bi-spinor spin-parity local correlations. ANNALS OF PHYSICS, v. 395, p. 301-316, AUG 2018. (18/03960-9, 17/02294-2)

FERNANDO E SILVA, CAIO; BERNARDINI, ALEX E.. Intrinsic quantum correlations for Gaussian localized Dirac cat states in phase space. Physical Review A, v. 104, n. 5, NOV 17 2021. (18/03960-9)