Edge switch transformation in microwave networks

Lipovský²,

Białous³

et al. 2021

Phys. Rev. E

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We investigate experimentally a Fermi golden rule in two-edge and five-edge microwave networks with preserved time reversal invariance. A Fermi golden rule gives rates of decay of states obtained by perturbing embedded eigenvalues of graphs and networks. We show that the embedded eigenvalues are connected with the topological resonances of the analyzed systems and we find the trajectories of the topological resonances in the complex plane.

Section: Simulation Of Quantum Graphs By Microwave Networkmentioning

confidence: 99%

Application of topological resonances in experimental investigation of a Fermi golden rule in microwave networks

Lipovský²,

Białous³

et al. 2021

Phys. Rev. E

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“…In the experimental investigation of properties of quantum graphs, we used microwave networks simulating quantum graphs [16,[24][25][26][27][28][29]. The emulation of quantum graphs by microwave networks is possible because of the formal analogy of the one-dimensional Schrödinger equation describing quantum graphs and the telegrapher's equation for microwave networks [24,26].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Euler Characteristics of the Graphs Split at Vertices

Farooq

Akhshani

et al. 2022

Entropy

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We show that there is a relationship between the generalized Euler characteristic Eo(|VDo|) of the original graph that was split at vertices into two disconnected subgraphs i=1,2 and their generalized Euler characteristics Ei(|VDi|). Here, |VDo| and |VDi| denote the numbers of vertices with the Dirichlet boundary conditions in the graphs. The theoretical results are experimentally verified using microwave networks that simulate quantum graphs. We demonstrate that the evaluation of the generalized Euler characteristics Eo(|VDo|) and Ei(|VDi|) allow us to determine the number of vertices where the two subgraphs were initially connected.

“…The chiral orthogonal, unitary, and symplectic ensembles 34 have been recently realized using microwave networks. Microwave networks have been also used to study a topological edge invariant 35 , 36 and the photon number statistics of coherent light 37 . Therefore, microwave networks as well as flat microwave cavities 38 – 47 and Rydberg atoms strongly driven by microwave fields 48 – 51 have become one of the most important model systems, that are successfully used in experimental modeling of complex quantum systems.…”

Section: Introductionmentioning

confidence: 99%

A new spectral invariant for quantum graphs

Kurasov

Bauch

et al. 2021

Sci Rep

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The Euler characteristic i.e., the difference between the number of vertices |V| and edges |E| is the most important topological characteristic of a graph. However, to describe spectral properties of differential equations with mixed Dirichlet and Neumann vertex conditions it is necessary to introduce a new spectral invariant, the generalized Euler characteristic $$\chi _G:= |V|-|V_D|-|E|$$ χ G : = | V | - | V D | - | E | , with $$|V_D|$$ | V D | denoting the number of Dirichlet vertices. We demonstrate theoretically and experimentally that the generalized Euler characteristic $$\chi _G$$ χ G of quantum graphs and microwave networks can be determined from small sets of lowest eigenfrequencies. If the topology of the graph is known, the generalized Euler characteristic $$\chi _G$$ χ G can be used to determine the number of Dirichlet vertices. That makes the generalized Euler characteristic $$\chi _G$$ χ G a new powerful tool for studying of physical systems modeled by differential equations on metric graphs including isoscattering and neural networks where both Neumann and Dirichlet boundary conditions occur.