Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption

• URL: http://arxiv.org/abs/2212.01566v1
• Date: Sat, 3 Dec 2022 07:53:19 GMT
• Title: Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption
• Authors: Michal Lawniczak, Afshin Akhshani, Omer Farooq, Malgorzata Bialous, Szymon Bauch, Barbara Dietz, and Leszek Sirko
• Abstract summary: We report on experimental studies of the distribution of the reflection coefficients and the imaginary and real parts of Wigner's reaction (K) matrix. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random matrix theory (RMT) We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph, does not have any visible effects on the distributions of the reflection coefficients and the K and S matrices associated with the corresponding open quantum graph.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic systems and the two-point correlation function of the S-matrix elements. The analytical results and the Monte Carlo simulations depend on the size of absorption. To verify them, we performed experiments with microwave networks for various absorption strengths. We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph, and attributed to the presence of nonuniversal short periodic orbits, does not have any visible effects on the distributions of the reflection coefficients and the K and S matrices associated with the corresponding open quantum graph.

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