Closed and open superconducting microwave waveguide networks as a model for quantum graphs
arXiv:2401.16031 · doi:10.1103/PhysRevE.109.034201
Abstract
We report on high-precision measurements that were performed with superconducting waveguide networks with the geometry of a tetrahedral and a honeycomb graph. They consist of junctions of valency three that connect straight rectangular waveguides of incommensurable lengths. The experiments were performed in the frequency range of a single transversal mode, where the associated Helmholtz equation is effectively one dimensional and waveguide networks may serve as models of quantum graphs with the joints and waveguides corresponding to the vertices and bonds. The tetrahedral network comprises T junctions, while the honeycomb network exclusively consists of Y junctions, that join waveguides with relative angles 90 degree and 120 degree, respectively. We demonstrate that the vertex scattering matrix, which describes the propagation of the modes through the junctions strongly depends on frequency and is non-symmetric at a T junction and thus differs from that of a quantum graph with Neumann boundary conditions at the vertices. On the contrary, at a Y junction, similarity can be achieved in a certain frequeny range. We investigate the spectral properties of closed waveguide networks and fluctuation properties of the scattering matrix of open ones and find good agreement with random matrix theory predictions for the honeycomb waveguide graph.
References in corpus (17)
- Localization of interacting fermions at high temperature
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
- Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards
- Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
- Power spectrum analysis and missing level statistics of microwave graphs with violated time reversal invariance
- Experimental and numerical investigation of the reflection coefficient and the distributions of Wigner's reaction matrix for irregular graphs with absorption
- Spectral fluctuations and 1/f noise in the order-chaos transition regime
- In-situ Broadband Cryogenic Calibration for Two-port Superconducting Microwave Resonators
- Non-Weyl Microwave Graphs
- Induced Time-Reversal Symmetry Breaking Observed in Microwave Billiards
- Spectral statistics in an open parametric billiard system
- Chaotic Scattering in the Regime of Weakly Overlapping Resonances
- Quantum graphs where back-scattering is prohibited
- Bound States in Sharply Bent Waveguides: Analytical and Experimental Approach
- Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison
- Resonances and poles in isoscattering microwave networks and graphs