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. 2019 Mar 11;9:4156. doi: 10.1038/s41598-019-39281-4

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© The Author(s) 2019

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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Spectral function related to the vacuum state |0,−〉 of the 2 γQRM in correspondence of the collapse point g/ω = 0.5, at different values of ω₀. It can be seen that the position of the isolated ground state is dependent on the value of the atomic frequency. In all cases ε = 0.0005 (see Eq. (12)), while the truncation number exploited for the continued fraction is N = 8000.