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arXiv · 2512.03717

Geometrical structure of the Wigner flow information quantifiers and hyperbolic stability in the phase-space framework

Alex E. Bernardini
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Abstract

Quantifiers of stationarity, classicality, purity and vorticity are derived from phase-space differential geometrical structures within the Weyl-Wigner framework, after which they are related to the hyperbolic stability of classical and quantum-modified Hamiltonian (non-linear) equations of motion. By examining the equilibrium regime produced by such an autonomous system of ordinary differential equations, a correspondence between Wigner flow properties and hyperbolic stability boundaries in the phase-space is identified. Explicit analytical expressions for equilibrium-stability parameters are obtained for quantum Gaussian ensembles, wherein information quantifiers driven by Wigner currents are identified. Illustrated by an application to a Harper-like system, the results provide a self-contained analysis for identifying the influence of quantum fluctuations associated to the emergence of phase-space vorticity in order to quantify equilibrium and stability properties of Hamiltonian non-linear dynamics.

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Alex E. Bernardini. 2025-12-03. Geometrical structure of the Wigner flow information quantifiers and hyperbolic stability in the phase-space framework. https://arxiv.org/abs/2512.03717

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