Geometrical structure of the Wigner flow information quantifiers and hyperbolic stability in the phase-space framework
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915651412557824 |
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| author | Bernardini, Alex E. |
| author_facet | Bernardini, Alex E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03717 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometrical structure of the Wigner flow information quantifiers and hyperbolic stability in the phase-space framework Bernardini, Alex E. Quantum Physics 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. |
| title | Geometrical structure of the Wigner flow information quantifiers and hyperbolic stability in the phase-space framework |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.03717 |