Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically g...
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MDPI AG
2020-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/11/1219 |
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| author | Zeyi Shi Sumiyoshi Abe |
| author_facet | Zeyi Shi Sumiyoshi Abe |
| author_sort | Zeyi Shi |
| collection | DOAJ |
| description | Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini–Kossakowski–Lindblad–Sudarshan equation. |
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| format | Article |
| id | doaj.art-8e1bb592a6b64c15b1a79fba2bcad3a3 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T15:19:52Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-8e1bb592a6b64c15b1a79fba2bcad3a32023-11-20T18:37:14ZengMDPI AGEntropy1099-43002020-10-012211121910.3390/e22111219Quantum Weak Invariants: Dynamical Evolution of Fluctuations and CorrelationsZeyi Shi0Sumiyoshi Abe1Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, ChinaDepartment of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, ChinaWeak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a completely positive map, the fluctuations monotonically grow even if the map is not unital, in contrast to the fact that monotonic increases of both the von Neumann entropy and Rényi entropy require the map to be unital. In this way, the weak invariants describe temporal asymmetry in a manner different from the entropies. A formula is presented for time evolution of the covariance matrix associated with the weak invariants in cases where the system density matrix obeys the Gorini–Kossakowski–Lindblad–Sudarshan equation.https://www.mdpi.com/1099-4300/22/11/1219monotonic growth of fluctuations of weak invariantsvon Neumann and Rényi entropiescompletely positive mapsGorini–Kossakowski–Lindblad–Sudarshan equationcovariance matrix |
| spellingShingle | Zeyi Shi Sumiyoshi Abe Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations Entropy monotonic growth of fluctuations of weak invariants von Neumann and Rényi entropies completely positive maps Gorini–Kossakowski–Lindblad–Sudarshan equation covariance matrix |
| title | Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations |
| title_full | Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations |
| title_fullStr | Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations |
| title_full_unstemmed | Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations |
| title_short | Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations |
| title_sort | quantum weak invariants dynamical evolution of fluctuations and correlations |
| topic | monotonic growth of fluctuations of weak invariants von Neumann and Rényi entropies completely positive maps Gorini–Kossakowski–Lindblad–Sudarshan equation covariance matrix |
| url | https://www.mdpi.com/1099-4300/22/11/1219 |
| work_keys_str_mv | AT zeyishi quantumweakinvariantsdynamicalevolutionoffluctuationsandcorrelations AT sumiyoshiabe quantumweakinvariantsdynamicalevolutionoffluctuationsandcorrelations |