Classical-Quantum correspondence in Lindblad evolution
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916294975029248 |
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| author | Galkowski, Jeffrey Huang, Zhen Zworski, Maciej |
| author_facet | Galkowski, Jeffrey Huang, Zhen Zworski, Maciej |
| contents | We show that for the Lindblad evolution defined using (at most) quadratically growing classical Hamiltonians and (at most) linearly growing classical jump functions (quantized into jump operators assumed to satisfy certain ellipticity conditions and modeling interaction with a larger system), the evolution of a quantum observable remains close to the classical Fokker--Planck evolution in the Hilbert--Schmidt norm for times vastly exceeding the Ehrenfest time (the limit of such agreement with no jump operators). The time scale is the same as in the recent papers by Hernández--Ranard--Riedel but the statement and methods are different. The appendix presents numerical experiments illustrating the classical/quantum correspondence in Lindblad evolution and comparing it to the mathematical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classical-Quantum correspondence in Lindblad evolution Galkowski, Jeffrey Huang, Zhen Zworski, Maciej Mathematical Physics Analysis of PDEs Quantum Physics We show that for the Lindblad evolution defined using (at most) quadratically growing classical Hamiltonians and (at most) linearly growing classical jump functions (quantized into jump operators assumed to satisfy certain ellipticity conditions and modeling interaction with a larger system), the evolution of a quantum observable remains close to the classical Fokker--Planck evolution in the Hilbert--Schmidt norm for times vastly exceeding the Ehrenfest time (the limit of such agreement with no jump operators). The time scale is the same as in the recent papers by Hernández--Ranard--Riedel but the statement and methods are different. The appendix presents numerical experiments illustrating the classical/quantum correspondence in Lindblad evolution and comparing it to the mathematical results. |
| title | Classical-Quantum correspondence in Lindblad evolution |
| topic | Mathematical Physics Analysis of PDEs Quantum Physics |
| url | https://arxiv.org/abs/2403.09345 |