Analysis of Missing Level Statistics for Microwave Networks Simulating Quantum Chaotic Graphs Without Time Reversal Symmetry - the Case of Randomly Lost Resonances

Ławniczak, Michał; Białous, Małgorzata; Yunko, Vitalii; Bauch, Szymon; Dietz, Barbara; Sirko, Leszek

doi:10.12693/aphyspola.132.1672

Cited by 14 publications

(8 citation statements)

References 63 publications

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“…It is attainable because both systems are described by the same equations: the one-dimensional Schrödinger equation appearing in quantum graphs is formally equivalent to the telegrapher's equation for microwave networks [13,16]. Microwave networks, as the only ones, allow for the experimental simulation of quantum systems corresponding to all three classical ensembles in the random-matrix theory (RMT): the systems with T invariance belonging to Gaussian orthogonal ensemble (GOE) [13-15, 17, 19] and Gaussian symplectic ensemble (GSE) [20], and the systems without T invariance belonging to Gaussian unitary ensemble (GUE) [13,18,[21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Hearing Euler characteristic of graphs

et al. 2020

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The Euler characteristic χ = |V | − |E| and the total length L are the most important topological and geometrical characteristics of a metric graph. Here, |V | and |E| denote the number of vertices and edges of a graph. The Euler characteristic determines the number β of independent cycles in a graph while the total length determines the asymptotic behavior of the energy eigenvalues via the Weyl's law. We show theoretically and confirm experimentally that the Euler characteristic can be determined (heard) from a finite sequence of the lowest eigenenergies λ 1 ,. .. , λ N of a simple quantum graph, without any need to inspect the system visually. In the experiment quantum graphs are simulated by microwave networks. We demonstrate that the sequence of the lowest resonances of microwave networks with β ≤ 3 can be directly used in determining whether a network is planar, i.e., can be embedded in the plane. Moreover, we show that the measured Euler characteristic χ can be used as a sensitive revealer of the fully connected graphs.

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Section: Introductionmentioning

confidence: 99%

Hearing Euler characteristic of graphs

et al. 2020

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“…The microwave networks (graphs) simulate quantum graphs 8,9,13 because there is a direct analogy between the telegraph equation describing a microwave network and the Schrödinger equation of the corresponding quantum graph 5,24 . This is the only system which allows for the experimental simulation of quantum systems corresponding to all three classical ensembles in the random-matrix theory (RMT): with T invariance belonging to Gaussian orthogonal ensemble (GOE) 5,17,25,26 and Gaussian symplectic ensemble (GSE) 27 as well as systems without T invariance belonging to Gaussian unitary ensemble (GUE) 5,6,28–30 .…”

Section: Introductionmentioning

confidence: 99%

Investigation of the diagonal elements of the Wigner’s reaction matrix for networks with violated time reversal invariance

Ławniczak

Sirko

2019

Sci Rep

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The distributions of the diagonal elements of the Wigner’s reaction matrix for open systems with violated time reversal T invariance in the case of large absorption are for the first time experimentally studied. The Wigner’s reaction matrix links the properties of chaotic systems with the scattering processes in the asymptotic region. Microwave networks consisting of microwave circulators were used in the experiment to simulate quantum graphs with violated T invariance. The distributions of the diagonal elements of the reaction matrix were experimentally evaluated by measuring of the two-port scattering matrix . The violation of T invariance in the networks with large absorption was demonstrated by calculating the enhancement factor W of the matrix . Our experimental results are in very good agreement with the analytic ones attained for the Gaussian unitary ensemble in the random matrix theory. The obtained results suggest that the distributions P ( ʋ ) and P ( u ) of the imaginary and the real parts of the diagonal elements of the Wigner’s reaction matrix together with the enhancement factor W can be used as a powerful tool for identification of systems with violated T symmetry and quantification of their absorption.

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“…The power spectrum and the power law behavior were studied numerically in [56][57][58][59]. The usefulness of the power spectrum in analyzing experimental results was confirmed in [42] -measurements of molecular resonances and in the investigations of microwave networks [36,37,60], and billiards [61].…”

Section: Systemsmentioning

confidence: 99%

Experimental and Numerical Study of Spectral Properties of Three-Dimensional Chaotic Microwave Cavities: The Case of Missing Levels

Yunko

Białous

Bauch

et al. 2019

11th Chaotic Modeling and Simulation International Conference

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We present an experimental and numerical study of missing-level statistics of chaotic threedimensional microwave cavities. The nearest-neighbor spacing distribution, the spectral rigidity, and the power spectrum of level fluctuations were investigated. We show that the theoretical approach to a problem of incomplete spectra does not work well when the incompleteness of the spectra is caused by unresolved resonances. In such a case the fraction of missing levels can be evaluated by calculations based on random matrix theory.

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Analysis of Missing Level Statistics for Microwave Networks Simulating Quantum Chaotic Graphs Without Time Reversal Symmetry - the Case of Randomly Lost Resonances

Cited by 14 publications

References 63 publications

Hearing Euler characteristic of graphs

Hearing Euler characteristic of graphs

Investigation of the diagonal elements of the Wigner’s reaction matrix for networks with violated time reversal invariance

Experimental and Numerical Study of Spectral Properties of Three-Dimensional Chaotic Microwave Cavities: The Case of Missing Levels

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