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. 2023 Jul 28;9(1):76. doi: 10.1038/s41534-023-00745-1

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© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 2 — a Energy curves in the phase space obtained with Eq. (2). The hyperbolic point is denoted as O, the center points are represented with blue diamonds, and the solid line intersecting at O is the separatrix. Points O, A–E mark the centers of the initial coherent states chosen for the quantum dynamics. b Evolution of the FOTOC, c Husimi entropy, and d survival probability as a function of time. The exponential [linear] curve with rate [slope] given by the Lyapunov exponent in Eq. (4) are indicated in (b)[c]. e Snapshots of the Husimi functions; each row refers to one of the six initial coherent states investigated, and each column to a different time, as indicated.