Families of isospectral and isoscattering quantum graphs
arXiv:2505.16621 · doi:10.1103/6yk9-17y3
Abstract
A concept of germ graphs and the M-function formalism are employed to construct large families of isospectral and isoscattering graphs. This approach represents a complete departure from the original approach pioneered by Sunada, where isospectral graphs are obtained as quotients of a certain large symmetric graph. Using the M-function formalism and the symmetries of the graph itself we construct isospectral and isoscattering pairs. In our novel approach isospectral pairs do not need to be embedded into a larger symmetric graph as in Sunada's approach. We demonstrate that the introduced formalism can also be extended to graphs with dissipation. The theoretical predictions are validated experimentally using microwave networks emulating open quantum graphs with dissipation.
References in corpus (31)
- Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
- Experimental simulation of quantum graphs by microwave networks
- Can One Hear the Shape of a Graph?
- Chaotic Scattering on Graphs
- 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
- Multi-walker discrete time quantum walks on arbitrary graphs, their properties, and their photonic implementation
- A microwave realization of the Gaussian symplectic ensemble
- Non-universality in the spectral properties of time-reversal invariant microwave networks and quantum graphs
- Statistics of Impedance, Local Density of States, and Reflection in Quantum Chaotic Systems with Absorption
- The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
- Explicitly solvable cases of one-dimensional quantum chaos
- Perfect Absorption in Complex Scattering Systems with or without Hidden Symmetries
- Band spectra of rectangular graph superlattices
- Universal statistics of the local Green's function in quantum chaotic systems with absorption
- Spectral properties of microwave graphs with local absorption
- Non-Weyl Microwave Graphs
- Universal Chaotic Scattering on Quantum Graphs
- Linear Representations and Isospectrality with Boundary Conditions
- Quantum walk coherences on a dynamical percolation graph
- Isospectrality in Chaotic Billiards
- Scattering from isospectral quantum graphs
- Statistics of Complex Wigner Time Delays as a counter of S-matrix poles: Theory and Experiment
- Departure of some parameter-dependent spectral statistics of irregular quantum graphs from Random Matrix Theory predictions
- A Random Necklace Model
- Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption
- Experimental investigation of distributions of the off-diagonal elements of the scattering and the Wigner's matrices for networks with broken time reversal invariance
- Resonances and poles in isoscattering microwave networks and graphs
- Distinguishing co-spectral quantum graphs by scattering
- A geometric construction of isospectral magnetic graphs
- Quantizing graphs, one way or two?