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- W3042351036 abstract "We investigated the spectra of resonances of four-vertex microwave networks simulating both quantum graphs with preserved and with partially violated time-reversal invariance before and after an edge switch operation. We show experimentally that under the edge switch operation, the spectra of the microwave networks with preserved time-reversal symmetry are level-1 interlaced, i.e., ${ensuremath{nu}}_{nensuremath{-}r}ensuremath{le}{stackrel{ifmmode tilde{}else ~{}fi{}}{ensuremath{nu}}}_{n}ensuremath{le}{ensuremath{nu}}_{n+r}$, where $r=1$, in agreement with the recent theoretical predictions of Aizenman et al. [M. Aizenman, H. Schanz, U. Smilansky, and S. Warzel, Acta Phys. Pol. A 132, 1699 (2017)]. Here, we denote by ${{{ensuremath{nu}}_{n}}}_{n=1}^{ensuremath{infty}}$ and ${{{stackrel{ifmmode tilde{}else ~{}fi{}}{ensuremath{nu}}}_{n}}}_{n=1}^{ensuremath{infty}}$ the spectra of microwave networks before and after the edge switch transformation. We demonstrate that the experimental distribution $P(mathrm{ensuremath{Delta}}N)$ of the spectral shift $mathrm{ensuremath{Delta}}N$ is close to the theoretical one. Furthermore, we show experimentally that in the case of the four-vertex networks with partially violated time-reversal symmetry, the spectra are level-1 interlaced. Our experimental results are supplemented by the numerical calculations performed for quantum graphs with violated time-reversal symmetry. In this case, the edge switch transformation also leads to the spectra which are level-1 interlaced. Moreover, we demonstrate that for microwave networks simulating graphs with violated time-reversal symmetry, the experimental distribution $P(mathrm{ensuremath{Delta}}N)$ of the spectral shift $mathrm{ensuremath{Delta}}N$ agrees, within the experimental uncertainty, with the numerical one." @default.
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- W3042351036 date "2020-07-14" @default.
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- W3042351036 title "Edge switch transformation in microwave networks" @default.
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- W3042351036 doi "https://doi.org/10.1103/physreve.102.012210" @default.
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