Spectral properties of microwave graphs with local absorption

Allgaier, Markus; Gehler, Stefan; Barkhofen, Sonja; Stöckmann, H.-J.; Kuhl, Ulrich

doi:10.1103/physreve.89.022925

Cited by 43 publications

(27 citation statements)

References 33 publications

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“…Accordingly, the fluctuation properties in the spectra of classically chaotic quantum graphs with and without T invariance are expected to coincide with those of random matrices from the GOE and the GUE, respectively. This was confirmed experimentally [10,11] for the nearest-neighbor spacing distribution using microwave networks [22][23][24][25][26].…”

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confidence: 51%

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Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

et al. 2016

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We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal invariance. On the basis of our data sets we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a procedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.g., nuclei or molecules, where one has to deal with the problem of missing levels. Introduction.-In the last decades the concept of quantum chaos, that is, the understanding of the features of the classical dynamics in terms of the spectral properties of the corresponding quantum system, like nuclei, atoms, molecules, quantum wires and dots or other complex systems [1][2][3], has been elaborated extensively. It has been established by now that the spectral properties of generic quantum systems with classically regular dynamics agree with those of Poissonian random numbers [4] while they coincide with those of the eigenvalues of random matrices [6] from the Gaussian orthogonal ensemble (GOE) and the Gaussian unitary ensemble (GUE) for classically chaotic systems with and without timereversal (T ) invariance [5], respectively, in accordance with the Bohigas-Giannoni-Schmit (BGS) conjecture [7].A multitude of studies with focus on problems from the field of quantum chaos have been performed by now theoretically and numerically. However, there are nongeneric features in the spectra of real physical systems that are not yet fully understood. Such problems are best tackled experimentally with the help of model systems like microwave billiards [8,9] and microwave graphs [10,11]. In the experiments with microwave billiards the analogy between the scalar Helmholtz equation and the Schrödinger equation of the corresponding quantum billiard is exploited. Microwave graphs [10,11] simulate the spectral properties of quantum graphs [12][13][14], networks of onedimensional wires joined at vertices. They provide an extremely rich system for the experimental and the theoretical study of quantum systems, that exhibit a chaotic dynamics in the classical limit.The idea of quantum graphs was introduced by Linus Pauling to model organic molecules [15] and they are also used to simulate, e.g., quantum wires [16], optical waveguides [17] and mesoscopic quantum systems [18,19]. The validity of the BGS conjecture was proven rigourously for graphs with incommensurable bond lengths in Refs. [20,21]. Accordingly, the fluctuation properties in the spectra of classically chaotic quantum graphs with and without T invariance are expected

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confidence: 51%

“…The effects of T violation on the spectral properties of the eigenvalues of closed quantum systems have also been investigated in such systems [35][36][37]. However, it is difficult if not impossible to obtain complete T violation in microwave billiards, whereas its achievement is straightforward in microwave networks [22][23][24][25][26].…”

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confidence: 99%

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

et al. 2016

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“…The BGS conjecture was proven rigourously for graphs with bonds of incommensurable lengths [44,45]. This was also confirmed experimentally with help of microwave networks [18][19][20][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 51%

“…The effects of breaking of time-reversal symmetry (TRS) on the spectral properties of the eigenvalues of closed quantum systems have also been investigated in such systems [31][32][33]. However, it is difficult if not impossible to obtain complete violation of TRS in microwave billiards, whereas its achievement in microwave networks [34][35][36][37][38] is straightforward.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2017

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We present experimental and numerical studies for level statistics in incomplete spectra obtained with microwave networks simulating quantum chaotic graphs with broken time reversal symmetry. We demonstrate that, if resonance frequencies are randomly removed from the spectra, the experimental results for the nearest-neighbor spacing distribution, the spectral rigidity and the average power spectrum are in good agreement with theoretical predictions for incomplete sequences of levels of systems with broken time reversal symmetry.

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“…This is possible because the Schrödinger equation describing a quantum graph is formally analogous to the telegraph's equation for signal propagation in a microwave network. It should be noticed that only microwave networks provide the experimental simulation of quantum systems representing all three symmetry classes in the random matrix theory (RMT), namely: systems with preserved time reversal symmetry (TRS) belonging to the Gaussian orthogonal ensemble (GOE, β = 1) [8,20,28,29], or to the Gaussian symplectic ensemble (GSE, β = 4) [30] and the systems with broken TRS belonging to the Gaussian unitary ensemble (GUE, β = 2) [8,18,[31][32][33]. One should generally mention that the model systems such as microwave networks [8,27,28,32,34], flat microwave cavities [35][36][37][38][39][40] and experiments using the Rydberg atoms strongly driven by microwave fields [41][42][43][44][45][46][47] appeared to be very successful in simplifying analysis of complex quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Wigner Reaction Matrix of Microwave Networks Simulating Quantum Graphs with Broken Time Reversal Symmetry-One-Port Investigation

et al. 2019

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We present new experimental studies of distributions of the Wigner reaction K matrix for open microwave networks. The one-port measurements were performed for the systems with broken time reversal symmetry in the regime of strong losses, where resonances are not resolved. Our studies are complementary to the previous two-port investigations. Fully connected six-vertex microwave networks were used to simulate quantum chaotic systems with broken time reversal symmetry. The usability of the distributions of the Wigner reaction K matrix as an effective tool for evaluation of losses in chaotic systems has been confirmed.

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Spectral properties of microwave graphs with local absorption

Cited by 43 publications

References 33 publications

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

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

Investigation of the Wigner Reaction Matrix of Microwave Networks Simulating Quantum Graphs with Broken Time Reversal Symmetry-One-Port Investigation

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