Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations |
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Authors: | Zeyi Shi Sumiyoshi Abe |
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Institution: | 1.Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China;2.Institute of Physics, Kazan Federal University, Kazan 420008, Russia;3.Department of Natural and Mathematical Sciences, Turin Polytechnic University in Tashkent, Tashkent 100095, Uzbekistan;4.ESIEA, 9 Rue Vesale, 75005 Paris, France |
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Abstract: | 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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Keywords: | monotonic growth of fluctuations of weak invariants von Neumann and Ré nyi entropies completely positive maps Gorini– Kossakowski– Lindblad– Sudarshan equation covariance matrix |
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