Quantum correlations for localized Dirac-like systems and Weyl-Wigner quantum mechanics extensions to non-linear systems

• Grant number: 23/00392-8
• Support Opportunities: Regular Research Grants
• Duration: June 01, 2023 - May 31, 2025
• 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 steps closely connected to each other by the Weyl-Wigner formalism of Quantum Mechanics in phase space. We first resort to formal fundamental structures to describe intrinsic and extrinsic characters of decoherence, non-classicality, locality, and correlations between two quantum modes (in continuous variables) of Dirac-type quantum systems that exhibit some localization characteristic. The subject is the evolution of the quantum correlation behavior constrained by localization effects, i. e. decoherence and entanglement -- {\em which includes sudden death and revivals}. Results are expected from a preliminary analysis of Dirac systems with Gaussian localization {\em Schr\"odinger cat} systems. From a phenomenological point of view, we assume that quantum information content is possible to be stored by quantum states in double layer graphene through its $SU(2) \otimes SU(2)$ {\em lattice-layer} structure which was already accommodated in the Dirac spinors formalism in previous works. However, from now, the inclusion of localization elements in the phase space becomes relevant. Therefore, we find out how to implement these properties according to Wigner's formalism.The second strand of this project deals with phase-space Wigner flow characteristics for generic $1$-dim systems with Hamiltonian, $H^{W} (q, \, p)$, constrained by $ \partial^2 H^ {W}/\partial q \partial p = 0$. Analytically, through Wigner functions and currents, we aim to describe the differential geometric structure of Wigner flow quantifiers, and their direct rapport with the properties of the dynamical system related to stationarity, classicality, purity and vorticity. We expect that the correspondence with the equilibrium properties in terms of hyperbolic stability parameters can also be established, in order to quantitatively ascertain what might be the quantum effects on the equilibrium and stability conditions of a nonlinear system with established classical dynamics. In addition to seeking a generalized background formulation, as a phenomenological test platform for our theoretical developments, we shall consider Aubry-André-Harper type systems in our analysis. (AU)

Scientific publications

(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.; BERTOLAMI, O.. Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics. PHYSICAL REVIEW E, v. 107, n. 4, p. 11-pg., 2023-04-27. (20/01976-5, 23/00392-8)

FERNANDO E SILVA, CAIO; BERNARDINI, ALEX E.. Revival patterns for Dirac cat states in a constant magnetic field. PHYSICAL REVIEW A, v. 107, n. 4, p. 17-pg., 2023-04-27. (23/00392-8)

BERNARDINI, A. E.; BERTOLAMI, O.. Quantum Prey-Predator Dynamics: A Gaussian Ensemble Analysis. FOUNDATIONS OF PHYSICS, v. 53, n. 3, p. 11-pg., 2023-06-01. (23/00392-8, 20/01976-5)