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Farooq O, Akhshani A, Ławniczak M, Białous M, Sirko L. Coupled unidirectional chaotic microwave graphs. Phys Rev E 2024; 110:014206. [PMID: 39160997 DOI: 10.1103/physreve.110.014206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2024] [Accepted: 06/28/2024] [Indexed: 08/21/2024]
Abstract
We experimentally investigate the undirected open microwave network Γ with internal absorption composed of two coupled directed halves, unidirectional networks Γ_{+} and Γ_{-}, corresponding to two possible directions of motion on their edges. The two-port scattering matrix of the network Γ is measured and the spectral statistics and the elastic enhancement factor of the network are evaluated. The comparison of the number of experimental resonances with the theoretical one predicted by the Weyl's law shows that within the experimental resolution the resonances are doubly degenerate. This conclusion was also corroborated by the numerical calculations. Though the network is characterized by the time-reversal symmetry, the missing level spectral statistics and the elastic enhancement factor are rather close to the Gaussian unitary ensemble predictions in random matrix theory. We used numerical calculations for the open nondissipative quantum graph possessing the same structure as the microwave network Γ to investigate the doublet structures in the spectrum which otherwise would not be experimentally resolved. We show that the doublet size distribution is close to the Poisson distribution.
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2
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Sol J, Röntgen M, Del Hougne P. Covert Scattering Control in Metamaterials with Non-Locally Encoded Hidden Symmetry. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023:e2303891. [PMID: 37726008 DOI: 10.1002/adma.202303891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2023] [Revised: 09/04/2023] [Indexed: 09/21/2023]
Abstract
Symmetries and tunability are of fundamental importance in wave scattering control, but symmetries are often obvious upon visual inspection, which constitutes a significant vulnerability of metamaterial wave devices to reverse-engineering risks. Here, it is theoretically and experimentally shown that a symmetry in the reduced basis of the "primary meta-atoms" that are directly connected to the outside world is sufficient; meanwhile, a suitable topology of non-local interactions between them, mediated by the internal "secondary" meta-atoms, can hide the symmetry from sight in the canonical basis. Covert symmetry-based scattering control in a cable-network metamaterial featuring a hidden parity ( P $\mathcal {P}$ ) symmetry in combination with hidden- P $\mathcal {P}$ -symmetry-preserving and hidden- P $\mathcal {P}$ -symmetry-breaking tuning mechanisms is experimentally demonstrated. Physical-layer security in wired communications is achieved using the domain-wise hidden P $\mathcal {P}$ -symmetry as a shared secret between the sender and the legitimate receiver. Within the approximation of negligible absorption, the first tuning of a complex scattering metamaterial without mirror symmetry to feature exceptional points (EPs) of PT $\mathcal {PT}$ -symmetric reflectionless states, as well as quasi-bound states in the continuum, is reported. These results are reproduced in metamaterials involving non-reciprocal interactions between meta-atoms, including the first observation of reflectionless EPs in a non-reciprocal system.
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Affiliation(s)
- Jérôme Sol
- INSA Rennes, CNRS, IETR-UMR 6164, F-35000, Rennes, France
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3
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Akhshani A, Białous M, Sirko L. Quantum graphs and microwave networks as narrow-band filters for quantum and microwave devices. Phys Rev E 2023; 108:034219. [PMID: 37849123 DOI: 10.1103/physreve.108.034219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/01/2023] [Accepted: 09/19/2023] [Indexed: 10/19/2023]
Abstract
We investigate properties of the transmission amplitude of quantum graphs and microwave networks composed of regular polygons such as triangles and squares. We show that for the graphs composed of regular polygons, with the edges of the length l, the transmission amplitude displays a band of transmission suppression with some narrow peaks of full transmission. The peaks are distributed symmetrically with respect to the symmetry axis kl=π, where k is the wave vector. For microwave networks the transmission peak amplitudes are reduced and their symmetry is broken due to the influence of internal absorption. We demonstrate that for the graphs composed of the same polygons but separated by the edges of length l^{'}
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Affiliation(s)
- Afshin Akhshani
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
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4
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Białous M, Dietz B, Sirko L. Experimental study of the elastic enhancement factor in a three-dimensional wave-chaotic microwave resonator exhibiting strongly overlapping resonances. Phys Rev E 2023; 107:054210. [PMID: 37328966 DOI: 10.1103/physreve.107.054210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/24/2023] [Indexed: 06/18/2023]
Abstract
We study the elastic enhancement factor and the two-point correlation function of the scattering matrix obtained from measurements of reflection and transmission spectra of a three-dimensional (3D) wave-chaotic microwave cavity in regions of moderate and large absorption. They are used to identify the degree of chaoticity of the system in the presence of strongly overlapping resonances, where other measures such as short- and long-range level correlations cannot be applied. The average value of the experimentally determined elastic enhancement factor for two scattering channels agrees well with random-matrix theory predictions for quantum chaotic systems, thus corroborating that the 3D microwave cavity exhibits the features of a fully chaotic system with preserved time-reversal invariance. To confirm this finding we analyzed spectral properties in the frequency range of lowest achievable absorption using missing-level statistics.
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Affiliation(s)
- Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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Ławniczak M, Akhshani A, Farooq O, Białous M, Bauch S, Dietz B, Sirko L. Distributions of the Wigner reaction matrix for microwave networks with symplectic symmetry in the presence of absorption. Phys Rev E 2023; 107:024203. [PMID: 36932527 DOI: 10.1103/physreve.107.024203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Accepted: 01/24/2023] [Indexed: 02/09/2023]
Abstract
We report on experimental studies of the distribution of the reflection coefficients, and the imaginary and real parts of Wigner's reaction (K) matrix employing open microwave networks with symplectic symmetry and varying size of absorption. The results are compared to analytical predictions derived for the single-channel scattering case within the framework of random-matrix theory (RMT). Furthermore, we performed Monte Carlo simulations based on the Heidelberg approach for the scattering (S) and K matrix of open quantum-chaotic systems and the two-point correlation function of the S-matrix elements. The analytical results and the Monte Carlo simulations depend on the size of absorption. To verify them, we performed experiments with microwave networks for various absorption strengths. We show that deviations from RMT predictions observed in the spectral properties of the corresponding closed quantum graph and attributed to the presence of nonuniversal short periodic orbits does not have any visible effects on the distributions of the reflection coefficients and the K and S matrices associated with the corresponding open quantum graph.
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Affiliation(s)
- Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Afshin Akhshani
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Omer Farooq
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Szymon Bauch
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China.,Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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6
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Białous M, Sirko L. Enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity. Phys Rev E 2022; 106:064208. [PMID: 36671148 DOI: 10.1103/physreve.106.064208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Accepted: 12/06/2022] [Indexed: 12/23/2022]
Abstract
We investigated properties of a singular billiard, that is, a quantum billiard which contains a pointlike (zero-range) perturbation. A singular billiard was simulated experimentally by a rectangular microwave flat resonator coupled to microwave power via wire antennas which act as singular scatterers. The departure from regularity was quantitatively estimated by the short-range plasma model in which the parameter η takes the values 1 and 2 for the Poisson and semi-Poisson statistics, respectively. We show that in the regime of semi-Poisson statistics the experimental power spectrum and the second nearest-neighbor-spacing distribution P(2,s) are in good agreement with their theoretical predictions. Furthermore, the measurement of the two-port scattering matrix allowed us to evaluate experimentally the enhancement factor F(γ^{tot}) in the regime of the semi-Poisson statistics as a function of the total absorption factor γ^{tot}. The experimental results were compared with the analytical formula for F(γ^{tot}) evaluated in this article. The agreement between the experiment and theory is good.
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Affiliation(s)
- Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
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Farooq O, Ławniczak M, Akhshani A, Bauch S, Sirko L. The Generalized Euler Characteristics of the Graphs Split at Vertices. ENTROPY 2022; 24:e24030387. [PMID: 35327898 PMCID: PMC8947457 DOI: 10.3390/e24030387] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/02/2022] [Revised: 02/25/2022] [Accepted: 03/08/2022] [Indexed: 12/10/2022]
Abstract
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.
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Chen L, Anlage SM, Fyodorov YV. Statistics of Complex Wigner Time Delays as a Counter of S-Matrix Poles: Theory and Experiment. PHYSICAL REVIEW LETTERS 2021; 127:204101. [PMID: 34860068 DOI: 10.1103/physrevlett.127.204101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2021] [Accepted: 10/15/2021] [Indexed: 06/13/2023]
Abstract
We study the statistical properties of the complex generalization of Wigner time delay τ_{W} for subunitary wave-chaotic scattering systems. We first demonstrate theoretically that the mean value of the Re[τ_{W}] distribution function for a system with uniform absorption strength η is equal to the fraction of scattering matrix poles with imaginary parts exceeding η. The theory is tested experimentally with an ensemble of microwave graphs with either one or two scattering channels and showing broken time-reversal invariance and variable uniform attenuation. The experimental results are in excellent agreement with the developed theory. The tails of the distributions of both real and imaginary time delay are measured and are also found to agree with theory. The results are applicable to any practical realization of a wave-chaotic scattering system in the short-wavelength limit, including quantum wires and dots, acoustic and electromagnetic resonators, and quantum graphs.
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Affiliation(s)
- Lei Chen
- Quantum Materials Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA
| | - Steven M Anlage
- Quantum Materials Center, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA
| | - Yan V Fyodorov
- Department of Mathematics, Kings College London, London WC26 2LS, United Kingdom
- L. D. Landau Institute for Theoretical Physics, Semenova 1a, 142432 Chernogolovka, Russia
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9
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Białous M, Dulian P, Sawicki A, Sirko L. Delay-time distribution in the scattering of short Gaussian pulses in microwave networks. Phys Rev E 2021; 104:024223. [PMID: 34525523 DOI: 10.1103/physreve.104.024223] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 08/06/2021] [Indexed: 11/07/2022]
Abstract
We investigate delay-time distributions in the scattering of short Gaussian pulses in microwave networks which simulate quantum graphs. We show that in the limit of short delay times the delay-time distribution is very sensitive to the internal structure of the networks. Therefore, it can be used to reveal their local structure including the boundary conditions at the vertices of the networks. In the frequency domain the pulses comprise many resonance frequencies of the networks. Furthermore, we show that the time-delay distribution averaged over different internal configurations of a finite network decays exponentially. Our experimental results for four-vertex and isoscattering microwave networks are in very good agreement with the theoretical ones obtained from the modified theory of U. Smilansky and H. Schanz [J. Phys. A 51, 075302 (2018)1751-811310.1088/1751-8121/aaa0df]. We modified the theory to account for internal absorption of microwave networks.
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Affiliation(s)
- Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Piotr Dulian
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Adam Sawicki
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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10
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Saleki Z, Majarshin AJ, Luo YA, Zhang DL. Spectral statistics of light in one-dimensional graphene-based photonic crystals. Phys Rev E 2021; 104:014116. [PMID: 34412324 DOI: 10.1103/physreve.104.014116] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2020] [Accepted: 06/07/2021] [Indexed: 11/07/2022]
Abstract
The optical properties and spectral statistics of light in one-dimensional photonic crystals in the representative classes of (AB)^{N} (composed of dielectric layers) and (AGBG)^{N} (composed of periodic stacking of graphene-dielectric layers) have been investigated using the transfer matrix method and random matrix theory. The proposed method provides new predictions to determine the chaos and regularity of the optical systems. In this analysis, the chaoticity parameter with q=0 for Poisson distribution and q→1 for Wigner distribution is determined based on the random matrix theory. It has been shown that two kinds of chaos and regularity modes can be found with Brody distribution. Also, as a part of this work, we found out the regular pattern in both classes of (AB)^{N} and (AGBG)^{N} when results were fit to a Brody distribution. Moreover, the effects of different parameters such as the number of unit cells, incident angle, state of polarization, and chemical potential of the graphene nanolayers on the structures' regularity are discussed. It is found that the regular patterns are seen in the band gaps. The results show that the structure (AGBG)^{N} has an extra photonic band gap compared to (AB)^{N}, which is tunable by changing the chemical potential of the graphene nanolayers. Therefore, the possibility of external control of the regularity using a gate voltage in the graphene-based photonic crystals is obtained. Finally, comparing of TE and TM waves based on the random matrix theory, which interpolates between regular and chaotic systems, indicates that the Poisson statistics well describes the TE waves.
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Affiliation(s)
- Ziba Saleki
- Department of Opto-Electronics and Information Engineering, College of Precision Instruments and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, People's Republic of China
| | - A J Majarshin
- School of Physics, Nankai University, Tianjin 300071, People's Republic of China
| | - Yan-An Luo
- School of Physics, Nankai University, Tianjin 300071, People's Republic of China
| | - De-Long Zhang
- Department of Opto-Electronics and Information Engineering, College of Precision Instruments and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, People's Republic of China
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11
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Ławniczak M, Kurasov P, Bauch S, Białous M, Akhshani A, Sirko L. A new spectral invariant for quantum graphs. Sci Rep 2021; 11:15342. [PMID: 34321508 PMCID: PMC8319202 DOI: 10.1038/s41598-021-94331-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Accepted: 07/08/2021] [Indexed: 11/08/2022] Open
Abstract
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 [Formula: see text], with [Formula: see text] denoting the number of Dirichlet vertices. We demonstrate theoretically and experimentally that the generalized Euler characteristic [Formula: see text] 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 [Formula: see text] can be used to determine the number of Dirichlet vertices. That makes the generalized Euler characteristic [Formula: see text] 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.
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Affiliation(s)
- Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland.
| | - Pavel Kurasov
- Department of Mathematics, Stockholm University, 106 91, Stockholm, Sweden.
| | - Szymon Bauch
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland
| | - Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland
| | - Afshin Akhshani
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland.
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12
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Białous M, Dietz B, Sirko L. Missing-level statistics in a dissipative microwave resonator with partially violated time-reversal invariance. Phys Rev E 2021; 103:052204. [PMID: 34134203 DOI: 10.1103/physreve.103.052204] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2021] [Accepted: 04/19/2021] [Indexed: 11/07/2022]
Abstract
We report on the experimental investigation of the fluctuation properties in the resonance frequency spectra of a flat resonator simulating a dissipative quantum billiard subject to partial time-reversal-invariance violation (TIV) which is induced by two magnetized ferrites. The cavity has the shape of a quarter bowtie billiard of which the corresponding classical dynamics is chaotic. Due to dissipation it is impossible to identify a complete list of resonance frequencies. Based on a random-matrix theory approach we derive analytical expressions for statistical measures of short- and long-range correlations in such incomplete spectra interpolating between the cases of preserved time-reversal invariance and complete TIV and demonstrate their applicability to the experimental spectra.
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Affiliation(s)
- Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
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Isoscattering strings of concatenating graphs and networks. Sci Rep 2021; 11:1575. [PMID: 33452312 PMCID: PMC7810996 DOI: 10.1038/s41598-020-80950-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2020] [Accepted: 12/30/2020] [Indexed: 11/08/2022] Open
Abstract
We identify and investigate isoscattering strings of concatenating quantum graphs possessing n units and 2n infinite external leads. We give an insight into the principles of designing large graphs and networks for which the isoscattering properties are preserved for \documentclass[12pt]{minimal}
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\begin{document}$$n \rightarrow \infty $$\end{document}n→∞. The theoretical predictions are confirmed experimentally using \documentclass[12pt]{minimal}
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\begin{document}$$n=2$$\end{document}n=2 units, four-leads microwave networks. In an experimental and mathematical approach our work goes beyond prior results by demonstrating that using a trace function one can address the unsettled until now problem of whether scattering properties of open complex graphs and networks with many external leads are uniquely connected to their shapes. The application of the trace function reduces the number of required entries to the \documentclass[12pt]{minimal}
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\begin{document}$$2n \times 2n $$\end{document}2n×2n scattering matrices \documentclass[12pt]{minimal}
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\begin{document}$${\hat{S}}$$\end{document}S^ of the systems to 2n diagonal elements, while the old measures of isoscattering require all \documentclass[12pt]{minimal}
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\begin{document}$$(2n)^2$$\end{document}(2n)2 entries. The studied problem generalizes a famous question of Mark Kac “Can one hear the shape of a drum?”, originally posed in the case of isospectral dissipationless systems, to the case of infinite strings of open graphs and networks.
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14
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Ławniczak M, van Tiggelen B, Sirko L. Experimental investigation of distributions of the off-diagonal elements of the scattering matrix and Wigner's K[over ̂] matrix for networks with broken time reversal invariance. Phys Rev E 2020; 102:052214. [PMID: 33327135 DOI: 10.1103/physreve.102.052214] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Accepted: 11/03/2020] [Indexed: 11/07/2022]
Abstract
We present an extensive experimental study of the distributions of the real and imaginary parts of the off-diagonal elements of the scattering matrix S[over ̂] and the Wigner's reaction K[over ̂] matrix for open microwave networks with broken time (T) reversal invariance. Microwave Faraday circulators were applied in order to break T invariance. The experimental distributions of the real and imaginary parts of the off-diagonal entries of the scattering matrix S[over ̂] are compared with the theoretical predictions from the supersymmetry random matrix theory [A. Nock, S. Kumar, H.-J. Sommers, and T. Guhr, Ann. Phys. (NY) 342, 103 (2014)10.1016/j.aop.2013.11.006]. Furthermore, we show that the experimental results are in very good agreement with the recent predictions for the distributions of the real and imaginary parts of the off-diagonal elements of the Wigner's reaction K[over ̂] matrix obtained within the framework of the Gaussian unitary ensemble of random matrix theory [S. B. Fedeli and Y. V. Fyodorov, J. Phys. A: Math. Theor. 53, 165701 (2020)1751-811310.1088/1751-8121/ab73ab]. Both theories include losses as tunable parameters and are therefore well adapted to the experimental verification.
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Affiliation(s)
- Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | | | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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15
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Chen L, Kottos T, Anlage SM. Perfect absorption in complex scattering systems with or without hidden symmetries. Nat Commun 2020; 11:5826. [PMID: 33203847 PMCID: PMC7673030 DOI: 10.1038/s41467-020-19645-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Accepted: 10/19/2020] [Indexed: 11/09/2022] Open
Abstract
Wavefront shaping (WFS) schemes for efficient energy deposition in weakly lossy targets is an ongoing challenge for many classical wave technologies relevant to next-generation telecommunications, long-range wireless power transfer, and electromagnetic warfare. In many circumstances these targets are embedded inside complicated enclosures which lack any type of (geometric or hidden) symmetry, such as complex networks, buildings, or vessels, where the hypersensitive nature of multiple interference paths challenges the viability of WFS protocols. We demonstrate the success of a general WFS scheme, based on coherent perfect absorption (CPA) electromagnetic protocols, by utilizing a network of coupled transmission lines with complex connectivity that enforces the absence of geometric symmetries. Our platform allows for control of the local losses inside the network and of the violation of time-reversal symmetry via a magnetic field; thus establishing CPA beyond its initial concept as the time-reversal of a laser cavity, while offering an opportunity for better insight into CPA formation via the implementation of semiclassical tools.
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Affiliation(s)
- Lei Chen
- Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, 20742, USA.
- Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA.
| | - Tsampikos Kottos
- Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, CT, 06459, USA
| | - Steven M Anlage
- Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, 20742, USA.
- Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA.
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Białous M, Dietz B, Sirko L. How time-reversal-invariance violation leads to enhanced backscattering with increasing openness of a wave-chaotic system. Phys Rev E 2020; 102:042206. [PMID: 33212639 DOI: 10.1103/physreve.102.042206] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2020] [Accepted: 09/23/2020] [Indexed: 06/11/2023]
Abstract
We report on the experimental investigation of the dependence of the elastic enhancement, i.e., enhancement of scattering in the backward direction over scattering in other directions, of a wave-chaotic system with partially violated time-reversal (T) invariance on its openness. The elastic enhancement factor is a characteristic of quantum chaotic scattering which is of particular importance in experiments, like compound-nuclear reactions, where only cross sections, i.e., the moduli of the associated scattering matrix elements, are accessible. In the experiment a quantum billiard with the shape of a quarter bow tie, which generates a chaotic dynamics, is emulated by a flat microwave cavity. Partial T-invariance violation of varying strength 0≤ξ≲1 is induced by two magnetized ferrites. The openness is controlled by increasing the number M of open channels, 2≤M≤9, while keeping the internal absorption unchanged. We investigate the elastic enhancement as function of ξ and find that for a fixed M it decreases with increasing T-invariance violation, whereas it increases with increasing openness beyond a certain value of ξ≳0.2. The latter result is surprising because it is opposite to that observed in systems with preserved Tinvariance (ξ=0). We come to the conclusion that the effect of T-invariance violation on the elastic enhancement then dominates over the openness, which is crucial for experiments which rely on enhanced backscattering, since, generally, a decrease of the openness is unfeasible. Motivated by these experimental results, we performed theoretical investigations based on random matrix theory which confirm our findings.
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Affiliation(s)
- Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Barbara Dietz
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
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Osman M, Fyodorov YV. Chaotic scattering with localized losses: S-matrix zeros and reflection time difference for systems with broken time-reversal invariance. Phys Rev E 2020; 102:012202. [PMID: 32794980 DOI: 10.1103/physreve.102.012202] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 06/15/2020] [Indexed: 11/07/2022]
Abstract
Motivated by recent studies of the phenomenon of coherent perfect absorption, we develop the random matrix theory framework for understanding statistics of the zeros of the (subunitary) scattering matrices in the complex energy plane, as well as of the recently introduced reflection time difference (RTD). The latter plays the same role for S-matrix zeros as the Wigner time delay does for its poles. For systems with broken time-reversal invariance, we derive the n-point correlation functions of the zeros in a closed determinantal form, and we study various asymptotics and special cases of the associated kernel. The time-correlation function of the RTD is then evaluated and compared with numerical simulations. This allows us to identify a cubic tail in the distribution of RTD, which we conjecture to be a superuniversal characteristic valid for all symmetry classes. We also discuss two methods for possible extraction of S-matrix zeros from scattering data by harmonic inversion.
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Affiliation(s)
- Mohammed Osman
- Department of Mathematics, King's College London, London WC26 2LS, United Kingdom
| | - Yan V Fyodorov
- Department of Mathematics, King's College London, London WC26 2LS, United Kingdom.,L. D. Landau Institute for Theoretical Physics, Semenova 1a, 142432 Chernogolovka, Russia
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18
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Del Hougne P, Savin DV, Legrand O, Kuhl U. Implementing nonuniversal features with a random matrix theory approach: Application to space-to-configuration multiplexing. Phys Rev E 2020; 102:010201. [PMID: 32795053 DOI: 10.1103/physreve.102.010201] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Accepted: 07/16/2020] [Indexed: 11/07/2022]
Abstract
We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is studied to quantify the channel diversity and to assess a specific system's performance. System-specific features such as unstirred field components give rise to nontrivial interchannel correlations and need to be properly accounted for in modeling based on random matrix theory. To address this challenge, we propose a two-step hybrid approach. Based on an ensemble of experimentally measured scattering matrices for different random metasurface configurations, we first learn a system-specific pair of coupling matrix and unstirred contribution to the Hamiltonian, and then add an appropriately weighted stirred contribution. We verify that our method is capable of reproducing the experimentally found distribution of the effective rank with good accuracy. The approach can also be applied to other wave phenomena in complex media.
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Affiliation(s)
- Philipp Del Hougne
- Institut de Physique de Nice, CNRS UMR 7010, Université Côte d'Azur, 06108 Nice, France
| | - Dmitry V Savin
- Department of Mathematics, Brunel University London, Uxbridge UB8 3PH, United Kingdom
| | - Olivier Legrand
- Institut de Physique de Nice, CNRS UMR 7010, Université Côte d'Azur, 06108 Nice, France
| | - Ulrich Kuhl
- Institut de Physique de Nice, CNRS UMR 7010, Université Côte d'Azur, 06108 Nice, France
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Yunko V, Białous M, Sirko L. Edge switch transformation in microwave networks. Phys Rev E 2020; 102:012210. [PMID: 32794898 DOI: 10.1103/physreve.102.012210] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 06/29/2020] [Indexed: 11/07/2022]
Abstract
We investigated the spectra of resonances of four-vertex microwave networks simulating both quantum graphs with preserved and with partially violated time-reversal invariance before and after an edge switch operation. We show experimentally that under the edge switch operation, the spectra of the microwave networks with preserved time-reversal symmetry are level-1 interlaced, i.e., ν_{n-r}≤ν[over ̃]_{n}≤ν_{n+r}, where r=1, in agreement with the recent theoretical predictions of Aizenman et al. [M. Aizenman, H. Schanz, U. Smilansky, and S. Warzel, Acta Phys. Pol. A 132, 1699 (2017)ATPLB60587-424610.12693/APhysPolA.132.1699]. Here, we denote by {ν_{n}}_{n=1}^{∞} and {ν[over ̃]_{n}}_{n=1}^{∞} the spectra of microwave networks before and after the edge switch transformation. We demonstrate that the experimental distribution P(ΔN) of the spectral shift ΔN is close to the theoretical one. Furthermore, we show experimentally that in the case of the four-vertex networks with partially violated time-reversal symmetry, the spectra are level-1 interlaced. Our experimental results are supplemented by the numerical calculations performed for quantum graphs with violated time-reversal symmetry. In this case, the edge switch transformation also leads to the spectra which are level-1 interlaced. Moreover, we demonstrate that for microwave networks simulating graphs with violated time-reversal symmetry, the experimental distribution P(ΔN) of the spectral shift ΔN agrees, within the experimental uncertainty, with the numerical one.
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Affiliation(s)
- Vitalii Yunko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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Ławniczak M, Kurasov P, Bauch S, Białous M, Yunko V, Sirko L. Hearing Euler characteristic of graphs. Phys Rev E 2020; 101:052320. [PMID: 32575246 DOI: 10.1103/physreve.101.052320] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2019] [Accepted: 05/07/2020] [Indexed: 11/07/2022]
Abstract
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 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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Affiliation(s)
- Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Pavel Kurasov
- Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden
| | - Szymon Bauch
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Vitalii Yunko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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