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This study explores microwave networks with absorption, revealing doubly degenerate resonances and spectral statistics aligning with Gaussian unitary ensemble predictions. Numerical analysis further supports these findings on spectral doublets.

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Area of Science:

  • Quantum chaos
  • Microwave network theory
  • Random matrix theory

Background:

  • Investigating complex networks with internal absorption is crucial for understanding wave phenomena.
  • Time-reversal symmetry in open systems often leads to specific spectral statistics.
  • Microwave networks serve as experimental platforms for quantum chaos studies.

Purpose of the Study:

  • To experimentally characterize an undirected open microwave network with internal absorption.
  • To evaluate spectral statistics and elastic enhancement factor.
  • To compare experimental findings with theoretical predictions, including Weyl's law and random matrix theory.

Main Methods:

  • Experimental measurement of the two-port scattering matrix for the microwave network.
  • Evaluation of spectral statistics and elastic enhancement factor from experimental data.
  • Numerical simulations of a corresponding open nondissipative quantum graph.

Main Results:

  • Experimental resonances were found to be doubly degenerate within experimental resolution.
  • Spectral statistics and elastic enhancement factor closely matched Gaussian unitary ensemble predictions.
  • Numerical calculations revealed doublet structures in the spectrum, with a Poisson distribution for doublet sizes.

Conclusions:

  • The investigated microwave network exhibits spectral properties influenced by its structure and absorption.
  • Doubly degenerate resonances and deviations from expected statistics highlight complex behaviors in open systems.
  • Numerical analysis provides insights into spectral features not fully resolved experimentally.