A spectral duality in graphs and microwave networks
arXiv:2110.11722 · doi:10.1103/PhysRevE.104.045211
Abstract
Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and charge conservation. Depending on the boundary conditions at the vertices, there are Neumann and Dirichlet graphs. The first ones are realized in experiments, since the standard junctions connecting the bonds obey Neumann boundary conditions due to current conservation. On average, the corresponding Neumann and Dirichlet eigenvalues alternate as a function of the wave number, with the consequence that the Neumann spectrum is described by random matrix theory only locally, but adopts features of the interlacing Dirichlet spectrum for long-range correlations. Another spectral interlacing is found for the Green's function, which in contrast to the secular determinant is experimentally accessible. This is illustrated by microwave studies and numerics.
arXiv comment8 pages, 5 figures
References in corpus (16)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
- Experimental simulation of quantum graphs by microwave networks
- Probability of Reflection by a Random Laser
- A microwave realization of the Gaussian symplectic ensemble
- Universal spectral statistics in quantum graphs
- Non-universality in the spectral properties of time-reversal invariant microwave networks and quantum graphs
- Perfect Absorption in Complex Scattering Systems with or without Hidden Symmetries
- Universal Quantum Graphs
- Topological Resonances in Scattering on Networks (Graphs)
- Non-Weyl Microwave Graphs
- Universal Chaotic Scattering on Quantum Graphs
- Spectra and spectral correlations of microwave graphs with symplectic symmetry
- GSE statistics without spin
- Statistical properties of resonance widths for open Quantum Graphs
- An elementary introduction to quantum graphs