Extended Weyl-Wigner phase-space framework for non-linear systems: typical and modified prey-predator-like dynamics
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914940450766848 |
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| author | Bernardini, Alex E. Bertolami, Orfeu |
| author_facet | Bernardini, Alex E. Bertolami, Orfeu |
| contents | The extension of the phase-space Weyl-Wigner quantum mechanics to the subset of Hamiltonians in the form of $H(q,\,p) = {K}(p) + {V}(q)$ (with $K(p)$ replacing single $p^2$ contributions) is revisited. Deviations from classical and stationary profiles are identified in terms of Wigner functions and Wigner currents for Gaussian and gamma/Laplacian distribution ensembles. The procedure is successful in accounting for the exact pattern of quantum fluctuations when compared with the classical phase-space pattern. General results are then specialized to some specific Hamiltonians revealing non-linear dynamics, and suggest a novel algorithm to treat quantum modifications mapped by Wigner currents. Our analysis shows that the framework encompasses, for instance, the quantized prey-predator-like scenarios subjected to statistical constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04291 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extended Weyl-Wigner phase-space framework for non-linear systems: typical and modified prey-predator-like dynamics Bernardini, Alex E. Bertolami, Orfeu Quantum Physics The extension of the phase-space Weyl-Wigner quantum mechanics to the subset of Hamiltonians in the form of $H(q,\,p) = {K}(p) + {V}(q)$ (with $K(p)$ replacing single $p^2$ contributions) is revisited. Deviations from classical and stationary profiles are identified in terms of Wigner functions and Wigner currents for Gaussian and gamma/Laplacian distribution ensembles. The procedure is successful in accounting for the exact pattern of quantum fluctuations when compared with the classical phase-space pattern. General results are then specialized to some specific Hamiltonians revealing non-linear dynamics, and suggest a novel algorithm to treat quantum modifications mapped by Wigner currents. Our analysis shows that the framework encompasses, for instance, the quantized prey-predator-like scenarios subjected to statistical constraints. |
| title | Extended Weyl-Wigner phase-space framework for non-linear systems: typical and modified prey-predator-like dynamics |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2409.04291 |