| Dedicated to the memory of Professor Mihail Megan
Mădălin Calamanciuc†, Aurelian Isar‡ Abstract: We review the results obtained by investigating, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups, the time evolution of quantum entanglement of two different bimodal systems, each one interacting with a thermal environment. The first system is formed of the free massless bosonic mode of a stationary observer in a region that is asymptotically flat (Kruskal observer) or freely falling in Schwarzschild black hole, and the mode of a uniformly accelerated observer hovering outside the event horizon of black hole. For initial bimodal Gaussian squeezed thermal states of the system, we show that under the influence of Hawking radiation the quantum entanglement of the two modes is destroyed in a finite time, for non-zero values of the temperature of the thermal environment, i.e. the phenomenon of entanglement sudden death takes place. The second system consists of two bosonic modes associated with a scalar quantum field in de Sitter space, characterized by two regions that are causally disconnected and described using open universe coordinates on two open charts. The survival time of the entanglement of this bimodal system strongly depends on the competition between the contrary effects provided by the squeezing of the initial bimodal state, the curvature of de Sitter space, the mass parameter and the thermal environment. It is shown that the entanglement is minimized for values 1/2 and 3/2 of the mass parameter, corresponding to the conformally coupled scalar field and, respectively, minimally coupled massless field. Keywords: quantum entanglement, Schwarzschild black hole, de Sitter space, Gaussian states, open systems. MSC: 81P42, 81V73, 81T20. DOI 10.56082/annalsarscimath.2026.3.205 Read full article *Accepted for publication on July 30, 2026 |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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