Wignerian symplectic covariance approach to the interaction-time problem
Abstract The concept of the symplectic covariance property of the Wigner distribution function and the symplectic invariance of the Wigner–Rényi entropies has been leveraged to estimate the interaction time of the moving quantum state in the presence of an absolutely integrable time-dependent potent...
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Nature Portfolio
2024-12-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-82744-6 |
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| author | D. Woźniak M. Kalka D. Kołaczek M. Wołoszyn B. J. Spisak |
| author_facet | D. Woźniak M. Kalka D. Kołaczek M. Wołoszyn B. J. Spisak |
| author_sort | D. Woźniak |
| collection | DOAJ |
| description | Abstract The concept of the symplectic covariance property of the Wigner distribution function and the symplectic invariance of the Wigner–Rényi entropies has been leveraged to estimate the interaction time of the moving quantum state in the presence of an absolutely integrable time-dependent potential. For this study, the considered scattering centre is represented initially by the Gaussian barrier. Two modifications of this potential energy are considered: a sudden change from barrier to barrier and from barrier to well. The scattering state is prepared in the form of a Schrödinger cat, and the Moyal equation governs its further time evolution. The whole analysis of the considered scattering problem is conducted in the above-barrier regime using the phase-space representation of quantum theory. The presented concept shifts the focus from the dynamics of the quantum state to a symplectically invariant state functions in the form of the Wigner–Rényi entropies of order one and one-half. These quantities serve as indicators of the beginning and end of the interaction of the non-Gaussian state with the sufficiently fast decaying potential representing the scattering centre. The presented approach is significant because it provides a new way to estimate the interaction time of moving quantum states with the dynamical scattering centre. Moreover, it allows for studying scattering processes in various physical systems, including atoms, molecules, and condensed matter systems. |
| format | Article |
| id | doaj-art-a41a99d3b93f4787814580f5bd22d5ce |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-a41a99d3b93f4787814580f5bd22d5ce2024-12-29T12:31:04ZengNature PortfolioScientific Reports2045-23222024-12-0114111510.1038/s41598-024-82744-6Wignerian symplectic covariance approach to the interaction-time problemD. Woźniak0M. Kalka1D. Kołaczek2M. Wołoszyn3B. J. Spisak4Faculty of Physics and Applied Computer Science, AGH University of KrakowFaculty of Physics and Applied Computer Science, AGH University of KrakowDepartment of Applied Mathematics, University of Agriculture in KrakówFaculty of Physics and Applied Computer Science, AGH University of KrakowFaculty of Physics and Applied Computer Science, AGH University of KrakowAbstract The concept of the symplectic covariance property of the Wigner distribution function and the symplectic invariance of the Wigner–Rényi entropies has been leveraged to estimate the interaction time of the moving quantum state in the presence of an absolutely integrable time-dependent potential. For this study, the considered scattering centre is represented initially by the Gaussian barrier. Two modifications of this potential energy are considered: a sudden change from barrier to barrier and from barrier to well. The scattering state is prepared in the form of a Schrödinger cat, and the Moyal equation governs its further time evolution. The whole analysis of the considered scattering problem is conducted in the above-barrier regime using the phase-space representation of quantum theory. The presented concept shifts the focus from the dynamics of the quantum state to a symplectically invariant state functions in the form of the Wigner–Rényi entropies of order one and one-half. These quantities serve as indicators of the beginning and end of the interaction of the non-Gaussian state with the sufficiently fast decaying potential representing the scattering centre. The presented approach is significant because it provides a new way to estimate the interaction time of moving quantum states with the dynamical scattering centre. Moreover, it allows for studying scattering processes in various physical systems, including atoms, molecules, and condensed matter systems.https://doi.org/10.1038/s41598-024-82744-6Symplectic covarianceTraversal timeWigner distribution functionSchrödinger cat stateWigner–Rényi entropy |
| spellingShingle | D. Woźniak M. Kalka D. Kołaczek M. Wołoszyn B. J. Spisak Wignerian symplectic covariance approach to the interaction-time problem Scientific Reports Symplectic covariance Traversal time Wigner distribution function Schrödinger cat state Wigner–Rényi entropy |
| title | Wignerian symplectic covariance approach to the interaction-time problem |
| title_full | Wignerian symplectic covariance approach to the interaction-time problem |
| title_fullStr | Wignerian symplectic covariance approach to the interaction-time problem |
| title_full_unstemmed | Wignerian symplectic covariance approach to the interaction-time problem |
| title_short | Wignerian symplectic covariance approach to the interaction-time problem |
| title_sort | wignerian symplectic covariance approach to the interaction time problem |
| topic | Symplectic covariance Traversal time Wigner distribution function Schrödinger cat state Wigner–Rényi entropy |
| url | https://doi.org/10.1038/s41598-024-82744-6 |
| work_keys_str_mv | AT dwozniak wigneriansymplecticcovarianceapproachtotheinteractiontimeproblem AT mkalka wigneriansymplecticcovarianceapproachtotheinteractiontimeproblem AT dkołaczek wigneriansymplecticcovarianceapproachtotheinteractiontimeproblem AT mwołoszyn wigneriansymplecticcovarianceapproachtotheinteractiontimeproblem AT bjspisak wigneriansymplecticcovarianceapproachtotheinteractiontimeproblem |