Closed and open superconducting microwave waveguide networks as a model for quantum graphs.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Waveguide Technology

Background:

• Superconducting waveguide networks can model quantum graphs.
• Understanding wave propagation in complex network geometries is crucial.

Purpose of the Study:

• To investigate the behavior of superconducting waveguide networks with tetrahedral and honeycomb geometries.
• To compare experimental results with quantum graph models and random matrix theory.

Main Methods:

• High-precision measurements on superconducting waveguide networks.
• Fabrication of tetrahedral and honeycomb network geometries with specific junction types (T and Y).
• Analysis of vertex scattering matrices and spectral properties.

Main Results:

• Vertex scattering matrices are frequency-dependent and asymmetric at T junctions.
• Y junctions exhibit frequency ranges of similarity to quantum graph models.
• Honeycomb networks show good agreement with random matrix theory predictions.

Conclusions:

• Superconducting waveguide networks serve as effective physical models for quantum graphs.
• Frequency dependence and junction geometry significantly influence wave propagation.
• Experimental findings align with theoretical predictions for specific network configurations.