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Plouraboué F. Quantum graph wave external triggering: Energy transfer and damping. Phys Rev E 2024; 109:054310. [PMID: 38907393 DOI: 10.1103/physreve.109.054310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2023] [Accepted: 02/19/2024] [Indexed: 06/24/2024]
Abstract
The propagation of wave trains resulting from a local external trigger inside a network described by a metric graph is analyzed using quantum graph theory. The external trigger is a finite-time perturbation imposed at one vertex of the graph, leading to a consecutive wave train into the network, supposedly at rest before the applied external perturbation. A complete analytical solution for the induced wave train is found having a specific spectrum as well as mode's amplitudes. Furthermore the precise condition by which the external trigger can transfer a maximal energy to any specific natural mode of the quantum graph is derived. Finally, the wave damping associated with boundary-layer dissipation is computed within a multiple time-scale asymptotic analysis. Exponential damping rates are explicitly found related to their corresponding mode's eigenvalue. Each mode energy is then obtained, as well as their exponential damping rate. The relevance of these results to the physics of waves within networks are discussed.
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2
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Dietz B, Klaus T, Masi M, Miski-Oglu M, Richter A, Skipa T, Wunderle M. Closed and open superconducting microwave waveguide networks as a model for quantum graphs. Phys Rev E 2024; 109:034201. [PMID: 38632749 DOI: 10.1103/physreve.109.034201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 02/08/2024] [Indexed: 04/19/2024]
Abstract
We report on high-precision measurements that were performed with superconducting waveguide networks with the geometry of a tetrahedral and a honeycomb graph. They consist of junctions of valency three that connect straight rectangular waveguides of equal width but incommensurable lengths. The experiments were performed in the frequency range of a single transversal mode, where the associated Helmholtz equation is effectively one-dimensional and waveguide networks may serve as models of quantum graphs with the joints and waveguides corresponding to the vertices and bonds. The tetrahedral network comprises T junctions, while the honeycomb network exclusively consists of Y junctions, that join waveguides with relative angles 90^{∘} and 120^{∘}, respectively. We demonstrate that the vertex scattering matrix, which describes the propagation of the modes through the junctions, strongly depends on frequency and is nonsymmetric at a T junction and thus differs from that of a quantum graph with Neumann boundary conditions at the vertices. On the other hand, at a Y junction, similarity can be achieved in a certain frequency range. We investigate the spectral properties of closed waveguide networks and fluctuation properties of the scattering matrix of open ones and find good agreement with random matrix theory predictions for the honeycomb waveguide graph.
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Affiliation(s)
- Barbara Dietz
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Korea
- Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Republic of Korea
| | - Tobias Klaus
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - Marco Masi
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - Maksym Miski-Oglu
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, D-64291 Darmstadt, Germany
| | - Achim Richter
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - Tatjana Skipa
- Darmstadt University of Applied Sciences, D-64295 Darmstadt, Germany
| | - Marcus Wunderle
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
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3
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Zhang X, Zhang W, Che J, Dietz B. Experimental test of the Rosenzweig-Porter model for the transition from Poisson to Gaussian unitary ensemble statistics. Phys Rev E 2023; 108:044211. [PMID: 37978640 DOI: 10.1103/physreve.108.044211] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2023] [Accepted: 09/20/2023] [Indexed: 11/19/2023]
Abstract
We report on an experimental investigation of the transition of a quantum system with integrable classical dynamics to one with violated time-reversal (T) invariance and chaotic classical counterpart. High-precision experiments are performed with a flat superconducting microwave resonator with circular shape in which T-invariance violation and chaoticity are induced by magnetizing a ferrite disk placed at its center, which above the cutoff frequency of the first transverse-electric mode acts as a random potential. We determine a complete sequence of ≃1000 eigenfrequencies and find good agreement with analytical predictions for the spectral properties of the Rosenzweig-Porter (RP) model, which interpolates between Poisson statistics expected for typical integrable systems and Gaussian unitary ensemble statistics predicted for chaotic systems with violated Tinvariance. Furthermore, we combine the RP model and the Heidelberg approach for quantum-chaotic scattering to construct a random-matrix model for the scattering (S) matrix of the corresponding open quantum system and show that it perfectly reproduces the fluctuation properties of the measured S matrix of the microwave resonator.
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Affiliation(s)
- Xiaodong Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Weihua Zhang
- 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
| | - Jiongning Che
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - 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
- Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Korea
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4
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Wang CZ, Kononchuk R, Kuhl U, Kottos T. Loss-Induced Violation of the Fundamental Transmittance-Asymmetry Bound in Nonlinear Complex Wave Systems. PHYSICAL REVIEW LETTERS 2023; 131:123801. [PMID: 37802952 DOI: 10.1103/physrevlett.131.123801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 08/28/2023] [Indexed: 10/08/2023]
Abstract
Nonlinearity-induced asymmetric transport (AT) can be utilized for on-chip implementation of nonreciprocal devices that do not require odd-vector biasing. This scheme, however, is subject to a fundamental bound dictating that the maximum transmittance asymmetry is inversely proportional to the asymmetry intensity range (AIR) over which AT occurs. Contrary to the conventional wisdom, we show that the implementation of losses can lead to an increase of the AIR without deteriorating the AT. We develop a general theory that provides a new upper bound for AT in nonlinear complex systems and highlights the importance of their structural complexity and of losses. Our predictions are confirmed numerically and experimentally using a microwave complex network of coaxial cables.
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Affiliation(s)
- Cheng-Zhen Wang
- Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Rodion Kononchuk
- Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Ulrich Kuhl
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 06200, Nice, France
| | - Tsampikos Kottos
- Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
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5
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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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6
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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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7
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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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8
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Riser R, Tian P, Kanzieper E. Power spectra and autocovariances of level spacings beyond the Dyson conjecture. Phys Rev E 2023; 107:L032201. [PMID: 37073062 DOI: 10.1103/physreve.107.l032201] [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: 03/02/2023] [Indexed: 04/20/2023]
Abstract
Introduced in the early days of random matrix theory, the autocovariances δI_{k}^{j}=cov(s_{j},s_{j+k}) of level spacings {s_{j}} accommodate detailed information on the correlations between individual eigenlevels. It was first conjectured by Dyson that the autocovariances of distant eigenlevels in the unfolded spectra of infinite-dimensional random matrices should exhibit a power-law decay δI_{k}^{j}≈-1/βπ^{2}k^{2}, where β is the symmetry index. In this Letter, we establish an exact link between the autocovariances of level spacings and their power spectrum, and show that, for β=2, the latter admits a representation in terms of a fifth Painlevé transcendent. This result is further exploited to determine an asymptotic expansion for autocovariances that reproduces the Dyson formula as well as provides the subleading corrections to it. High-precision numerical simulations lend independent support to our results.
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Affiliation(s)
- Roman Riser
- Department of Mathematics, Holon Institute of Technology, Holon 5810201, Israel
- Department of Physics and Research Center for Theoretical Physics and Astrophysics, University of Haifa, Haifa 3498838, Israel
| | - Peng Tian
- Department of Mathematics, Holon Institute of Technology, Holon 5810201, Israel
| | - Eugene Kanzieper
- Department of Mathematics, Holon Institute of Technology, Holon 5810201, Israel
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
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9
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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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10
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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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11
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Ma S, Antonsen TM, Anlage SM. Eigenfunction and eigenmode-spacing statistics in chaotic photonic crystal graphs. Phys Rev E 2022; 106:054215. [PMID: 36559373 DOI: 10.1103/physreve.106.054215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2021] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
The statistical properties of wave chaotic systems of varying dimensionalities and realizations have been studied extensively. These systems are commonly characterized by the statistics of the eigenmode spacings and the statistics of the eigenfunctions. Here, we propose photonic crystal (PC) defect waveguide graphs as a physical setting for chaotic graph studies. Photonic crystal waveguides possess a dispersion relation for the propagating modes, which is engineerable. Graphs constructed by joining these waveguides possess junctions and bends with distinct scattering properties. We present numerically determined statistical properties of an ensemble of such PC graphs including both eigenfunction amplitude and eigenmode-spacing studies. Our proposed system is compatible with silicon nanophotonic technology and opens chaotic graph studies to a new community of researchers.
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Affiliation(s)
- Shukai Ma
- Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Thomas M Antonsen
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742-3285, USA
| | - Steven M Anlage
- Quantum Materials Center, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742-3285, USA
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12
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Zhang W, Zhang X, Che J, Lu J, Miski-Oglu M, Dietz B. Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance. Phys Rev E 2022; 106:044209. [PMID: 36397497 DOI: 10.1103/physreve.106.044209] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that are connected at vertices. On the bonds, they are governed by the one-dimensional Schrödinger equation with boundary conditions imposed at the vertices. The resulting transport properties through the vertices may be expressed in terms of a vertex scattering matrix. Quantum graphs with incommensurate bond lengths attracted interest within the field of quantum chaos because, depending on the characteristics of the vertex scattering matrix, its wave dynamic may exhibit features of a typical quantum system with chaotic counterpart. In distinction to microwave networks, which serve as an experimental model of quantum graphs with Neumann boundary conditions, the vertex scattering matrices associated with a waveguide system depend on the wave number and the wave functions can be determined experimentally. We analyze the spectral properties of microwave waveguide systems with preserved and partially violated time-reversal invariance, and the properties of the associated wave functions. Furthermore, we study properties of the scattering matrix describing the measurement process within the framework of random matrix theory for quantum chaotic scattering systems.
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Affiliation(s)
- Weihua Zhang
- 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
| | - Xiaodong Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Jiongning Che
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Junjie Lu
- Institut de Physique de Nice, CNRS UMR 7010, Université Côte d'Azur, 06108 Nice, France
| | - M Miski-Oglu
- GSI Helmholtzzentrum für Schwerionenforschung GmbH D-64291 Darmstadt, Germany
| | - 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
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13
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Che J, Zhang X, Zhang W, Dietz B, Chai G. Fluctuation properties of the eigenfrequencies and scattering matrix of closed and open unidirectional graphs with chaotic wave dynamics. Phys Rev E 2022; 106:014211. [PMID: 35974604 DOI: 10.1103/physreve.106.014211] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Accepted: 07/04/2022] [Indexed: 06/15/2023]
Abstract
We present experimental and numerical results for the fluctuation properties in the eigenfrequency spectra and of the scattering matrix of closed and open unidirectional quantum graphs, respectively. Unidirectional quantum graphs, that are composed of bonds connected by reflectionless vertices, were introduced by Akila and Gutkin [Akila and Gutkin, J. Phys. A: Math. Theor. 48, 345101 (2015)1751-811310.1088/1751-8113/48/34/345101]. The nearest-neighbor spacing distribution of their eigenvalues was shown to comply with random-matrix theory predictions for typical chaotic systems with completely violated time-reversal invariance. The occurrence of short periodic orbits confined to a fraction of the system, that lead in conventional quantum graphs to deviations of the long-range spectral correlations from the behavior expected for typical chaotic systems, is suppressed in unidirectional ones. Therefore, we pose the question whether such graphs may serve as a more appropriate model for closed and open chaotic systems with violated time-reversal invariance than conventional ones. We compare the fluctuation properties of their eigenvalues and scattering matrix elements and observe especially in the long-range correlations larger deviations from random-matrix theory predictions for the unidirectional graphs. These are attributed to a loss of complexity of the underlying dynamic, induced by the unidirectionality.
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Affiliation(s)
- Jiongning Che
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Xiaodong Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Weihua Zhang
- 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
| | - 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
| | - Guozhi Chai
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
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14
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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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15
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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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16
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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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17
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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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18
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Bereczuk A, Dietz B, Che J, Kuipers J, Urbina JD, Richter K. Universal S-matrix correlations for complex scattering of wave packets in noninteracting many-body systems: Theory, simulation, and experiment. Phys Rev E 2021; 103:052209. [PMID: 34134298 DOI: 10.1103/physreve.103.052209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2020] [Accepted: 04/11/2021] [Indexed: 11/07/2022]
Abstract
We present an in-depth study of the universal correlations of scattering-matrix entries required in the framework of nonstationary many-body scattering of noninteracting indistinguishable particles where the incoming states are localized wave packets. Contrary to the stationary case, the emergence of universal signatures of chaotic dynamics in dynamical observables manifests itself in the emergence of universal correlations of the scattering matrix at different energies. We use a semiclassical theory based on interfering paths, numerical wave function based simulations, and numerical averaging over random-matrix ensembles to calculate such correlations and compare with experimental measurements in microwave graphs, finding excellent agreement. Our calculations show that the universality of the correlators survives the extreme limit of few open channels relevant for electron quantum optics, albeit at the price of dealing with large-cancellation effects requiring the computation of a large class of semiclassical diagrams.
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Affiliation(s)
- Andreas Bereczuk
- Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, 730000 Gansu, China
| | - Jiongning Che
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, 730000 Gansu, China
| | - Jack Kuipers
- Department of Biosystems Science and Engineering, ETH Zürich, 4058 Basel, Switzerland
| | - Juan-Diego Urbina
- Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
| | - Klaus Richter
- Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
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19
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López-González JL, Franco-Villafañe JA, Méndez-Sánchez RA, Zavala-Vivar G, Flores-Olmedo E, Arreola-Lucas A, Báez G. Deviations from Poisson statistics in the spectra of free rectangular thin plates. Phys Rev E 2021; 103:043004. [PMID: 34005940 DOI: 10.1103/physreve.103.043004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2020] [Accepted: 03/17/2021] [Indexed: 11/07/2022]
Abstract
The counterintuitive fact that wave chaos appears in the bending spectrum of free rectangular thin plates is presented. After extensive numerical simulations, varying the ratio between the length of its sides, it is shown that (i) frequency levels belonging to different symmetry classes cross each other and (ii) for levels within the same symmetry sector, only avoided crossings appear. The consequence of anticrossings is studied by calculating the distribution of the ratio of consecutive level spacings for each symmetry class. The resulting ratio distributions disagree with the expected Poissonian result. They are then compared with some well-known transition distributions between Poisson and the Gaussian orthogonal random matrix ensemble. It is found that the distribution of the ratio of consecutive level spacings agrees with the prediction of the Rosenzweig-Porter model. Also, the normal-mode vibration amplitudes are found experimentally on aluminum plates, before and after an avoided crossing for symmetrical-symmetrical, symmetrical-antisymmetrical, and antisymmetrical-symmetrical classes. The measured modes show an excellent agreement with our numerical predictions. The expected Poissonian distribution is recovered for the simply supported rectangular plate.
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Affiliation(s)
- J L López-González
- Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, SLP, México
| | - J A Franco-Villafañe
- CONACyT-Instituto de Física, Universidad Autónoma de San Luis Potosí, 78290, San Luis Potosí, SLP, México
| | - R A Méndez-Sánchez
- Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, P.O. Box 48-3, 62251 Cuernavaca, Mor. México
| | - G Zavala-Vivar
- Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Ciudad de México 02200, México
| | - E Flores-Olmedo
- Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Ciudad de México 02200, México
| | - A Arreola-Lucas
- Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Ciudad de México 02200, México
| | - G Báez
- Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana-Azcapotzalco, Ciudad de México 02200, México
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20
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Che J, Lu J, Zhang X, Dietz B, Chai G. Missing-level statistics in classically chaotic quantum systems with symplectic symmetry. Phys Rev E 2021; 103:042212. [PMID: 34005854 DOI: 10.1103/physreve.103.042212] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Accepted: 03/30/2021] [Indexed: 11/07/2022]
Abstract
We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend the random-matrix theory (RMT) approach introduced in Bohigas and Pato [O. Bohigas and M. P. Pato, Phys. Rev. E 74, 036212 (2006)PLEEE81539-375510.1103/PhysRevE.74.036212] for incomplete spectra of quantum systems with orthogonal symmetry. We validate these RMT predictions by randomly extracting a fraction of levels from complete sequences obtained numerically for quantum graphs and experimentally for microwave networks with symplectic symmetry and then apply them to incomplete experimental spectra to demonstrate their applicability. Independently of their symmetry class, quantum graphs exhibit nongeneric features which originate from nonuniversal contributions. Part of the associated eigenfrequencies can be identified in the level dynamics of parameter-dependent quantum graphs and extracted, thereby yielding spectra with systematically missing eigenfrequencies. We demonstrate that, even though the RMT approach relies on the assumption that levels are missing at random, it is possible to determine the fraction of missing levels and assign the appropriate symmetry class by comparison of their fluctuation properties with the RMT predictions.
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Affiliation(s)
- Jiongning Che
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Junjie Lu
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou University, Lanzhou, Gansu 730000, China.,Institut de Physique de Nice, CNRS UMR 7010, Université Côte d'Azur, 06108 Nice, France
| | - Xiaodong Zhang
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Barbara Dietz
- Lanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Guozhi Chai
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
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21
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Ławniczak M, Lipovský J, Białous M, Sirko L. Application of topological resonances in experimental investigation of a Fermi golden rule in microwave networks. Phys Rev E 2021; 103:032208. [PMID: 33862759 DOI: 10.1103/physreve.103.032208] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/29/2020] [Accepted: 03/02/2021] [Indexed: 11/07/2022]
Abstract
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 on the complex plane.
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Affiliation(s)
- Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Jiří Lipovský
- Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03 Hradec Králové, Czechia
| | - 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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22
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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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23
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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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24
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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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25
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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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26
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Lu J, Che J, Zhang X, Dietz B. Experimental and numerical investigation of parametric spectral properties of quantum graphs with unitary or symplectic symmetry. Phys Rev E 2020; 102:022309. [PMID: 32942473 DOI: 10.1103/physreve.102.022309] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2020] [Accepted: 07/29/2020] [Indexed: 11/07/2022]
Abstract
We present experimental and numerical results for the parametric fluctuation properties in the spectra of classically chaotic quantum graphs with unitary or symplectic symmetry. A level dynamics is realized by changing the lengths of a few bonds parametrically. The long-range correlations in the spectra reveal at a fixed parameter value deviations from those expected for generic chaotic systems with corresponding universality class. They originate from modes which are confined to individual bonds or explore only a fraction of the quantum graph. Similarly, discrepancies are observed in the avoided-crossing distribution, velocity correlation function, and the curvature distribution of the level dynamics which also may be attributed to such localized modes. We demonstrate that these may be easily identified by inspecting the level dynamics and consequently their nonuniversal contributions to the parametric spectral properties may be diminished considerably. This is corroborated by numerical studies.
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Affiliation(s)
- Junjie Lu
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Jiongning Che
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Xiaodong Zhang
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Barbara Dietz
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
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27
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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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28
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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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29
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Dietz B, Klaus T, Miski-Oglu M, Richter A, Wunderle M. Partial Time-Reversal Invariance Violation in a Flat, Superconducting Microwave Cavity with the Shape of a Chaotic Africa Billiard. PHYSICAL REVIEW LETTERS 2019; 123:174101. [PMID: 31702235 DOI: 10.1103/physrevlett.123.174101] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2019] [Indexed: 06/10/2023]
Abstract
We report on the experimental realization of a flat, superconducting microwave resonator, a microwave billiard, with partially violated time-reversal (T) invariance, induced by inserting a ferrite into the cavity and magnetizing it with an external magnetic field perpendicular to the resonator plane. In order to prevent its expulsion caused by the Meissner-Ochsenfeld effect, we used a cavity of which the top and bottom plate were made from niobium, a superconductor of type II, and cooled it down to liquid-helium temperature T_{LHe}≃4 K. The cavity had the shape of a chaotic Africa billiard. Superconductivity rendered possible the accurate determination of complete sequences of the resonance frequencies and of the widths and strengths of the resonances, an indispensable prerequisite for the unambiguous detection of T invariance violation, especially when it is only partially violated. This allows for the first time the precise specification of the size of T invariance violation from the fluctuation properties of the resonance frequencies and from the strength distribution, which actually depends sensitively on it and thus provides a most suitable measure. For this purpose we derived an analytical expression for the latter which is valid for isolated resonances in the range from no T invariance violation to complete violation.
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Affiliation(s)
- B Dietz
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - T Klaus
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - M Miski-Oglu
- GSI Helmholtzzentrum für Schwerionenforschung, GmbH D-64291 Darmstadt, Germany
| | - A Richter
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
| | - M Wunderle
- Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
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30
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Białous M, Dietz B, Sirko L. Experimental investigation of the elastic enhancement factor in a microwave cavity emulating a chaotic scattering system with varying openness. Phys Rev E 2019; 100:012210. [PMID: 31499840 DOI: 10.1103/physreve.100.012210] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Indexed: 11/07/2022]
Abstract
A characteristic of chaotic scattering is the excess of elastic over inelastic scattering processes quantified by the elastic enhancement factor F_{M}(T,γ), which depends on the number of open channels M, the average transmission coefficient T, and internal absorption γ. Using a microwave cavity with the shape of a chaotic quarter-bow-tie billiard, we study the elastic enhancement factor experimentally as a function of the openness, which is defined as the ratio of the Heisenberg time and the Weisskopf (dwell) time and is directly related to M and the size of internal absorption. In the experiments 2≤M≤9 open channels with an average transmission coefficient 0.34<T<0.98 and moderate internal absorption strength in the range of γ=0.9-2.8 are achieved. The experimental results for the enhancement factor are shown to agree well with random matrix theory predictions. Furthermore, in order to corroborate the wave-chaotic features of the microwave system, the spectral fluctuation properties are studied for M=2 channels. Agreement with those exhibited by typical, fully chaotic systems is illustrated, which is exemplary for the nearest-neighbor spacing distribution and the average power spectrum. Here we take into account the incompleteness of the sequence of resonance frequencies ascribed to the small yet nonvanishing internal absorption.
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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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31
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Ławniczak M, Lipovský J, Sirko L. Non-Weyl Microwave Graphs. PHYSICAL REVIEW LETTERS 2019; 122:140503. [PMID: 31050459 DOI: 10.1103/physrevlett.122.140503] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2018] [Indexed: 06/09/2023]
Abstract
One of the most important characteristics of a quantum graph is the average density of resonances, ρ=(L/π), where L denotes the length of the graph. This is a very robust measure. It does not depend on the number of vertices in a graph and holds also for most of the boundary conditions at the vertices. Graphs obeying this characteristic are called Weyl graphs. Using microwave networks that simulate quantum graphs we show that there exist graphs that do not adhere to this characteristic. Such graphs are called non-Weyl graphs. For standard coupling conditions we demonstrate that the transition from a Weyl graph to a non-Weyl graph occurs if we introduce a balanced vertex. A vertex of a graph is called balanced if the numbers of infinite leads and internal edges meeting at a vertex are the same. Our experimental results confirm the theoretical predictions of [E. B. Davies and A. Pushnitski, Analysis and PDE 4, 729 (2011)] and are in excellent agreement with the numerical calculations yielding the resonances of the networks.
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Affiliation(s)
- Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Jiří Lipovský
- Department of Physics, Faculty of Science, University of Hradec Králové, Rokitanského 62, 500 03 Hradec Králové, Czechia
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
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32
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Investigation of the diagonal elements of the Wigner's reaction matrix for networks with violated time reversal invariance. Sci Rep 2019; 9:5630. [PMID: 30948771 PMCID: PMC6449383 DOI: 10.1038/s41598-019-42123-y] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2018] [Accepted: 03/25/2019] [Indexed: 11/11/2022] Open
Abstract
The distributions of the diagonal elements of the Wigner’s reaction \documentclass[12pt]{minimal}
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\begin{document}$$\hat{K}$$\end{document}Kˆ 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 \documentclass[12pt]{minimal}
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\begin{document}$$\hat{K}$$\end{document}Kˆ matrix were experimentally evaluated by measuring of the two-port scattering matrix \documentclass[12pt]{minimal}
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\begin{document}$$\hat{S}$$\end{document}Sˆ. The violation of T invariance in the networks with large absorption was demonstrated by calculating the enhancement factor W of the matrix \documentclass[12pt]{minimal}
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\begin{document}$$\hat{S}$$\end{document}Sˆ. 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 \documentclass[12pt]{minimal}
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\begin{document}$$\hat{K}$$\end{document}Kˆ 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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Ławniczak M, Białous M, Yunko V, Bauch S, Sirko L. Missing-level statistics and analysis of the power spectrum of level fluctuations of three-dimensional chaotic microwave cavities. Phys Rev E 2018; 98:012206. [PMID: 30110821 DOI: 10.1103/physreve.98.012206] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2017] [Indexed: 06/08/2023]
Abstract
We present an experimental study of missing-level statistics of three-dimensional chaotic microwave cavities. The investigation is reinforced by the power spectrum of level fluctuations analysis, which also takes into account the missing levels. On the basis of our data sets we demonstrate that the power spectrum of level fluctuations in combination with short- and long-range spectral fluctuations provides a powerful tool for the determination of the fraction of randomly missing levels in systems that display wave chaos such as the three-dimensional chaotic microwave cavities. The experimental results are in good agreement with the analytical expressions that explicitly take into account the fraction of observed levels φ. We also show that in the case of incomplete spectra with many unresolved states the above procedures may fail. In such a case the random matrix theory calculations can be useful for the determination of missing levels.
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Affiliation(s)
- Michał Ławniczak
- 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
| | - Vitalii Yunko
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - Szymon Bauch
- 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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34
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Rehemanjiang A, Richter M, Kuhl U, Stöckmann HJ. Spectra and spectral correlations of microwave graphs with symplectic symmetry. Phys Rev E 2018; 97:022204. [PMID: 29548070 DOI: 10.1103/physreve.97.022204] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2017] [Indexed: 06/08/2023]
Abstract
Following an idea by Joyner et al. [Europhys. Lett. 107, 50004 (2014)EULEEJ0295-507510.1209/0295-5075/107/50004], a microwave graph with antiunitary symmetry T obeying T^{2}=-1 has been realized, thus mimicking a spin-1/2 system. The Kramers doublets expected for such systems have been clearly identified and could be lifted by a perturbation which breaks the antiunitary symmetry. The observed spectral level-spacing distribution of the Kramers doublets agreed with the predictions from the Gaussian symplectic ensemble (GSE), expected for chaotic systems with such a symmetry. In addition, we studied the random matrix equivalents of the used graphs both analytically and numerically. Here small deviations from the GSE level-spacing distribution were found, too small to be seen in the experiment but clearly visible in the simulations. Furthermore, results on the two-point correlation function, the spectral form factor, the number variance, and the spectral rigidity are presented, as well as on the transition from Gaussian symplectic to Gaussian orthogonal statistics by continuously changing T from T^{2}=-1 to T^{2}=1.
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Affiliation(s)
- A Rehemanjiang
- Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany
| | - M Richter
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (InPhyNi), 06108 Nice, France
| | - U Kuhl
- Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (InPhyNi), 06108 Nice, France
| | - H-J Stöckmann
- Fachbereich Physik der Philipps-Universität Marburg, D-35032 Marburg, Germany
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35
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Riser R, Osipov VA, Kanzieper E. Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems. PHYSICAL REVIEW LETTERS 2017; 118:204101. [PMID: 28581777 DOI: 10.1103/physrevlett.118.204101] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2017] [Indexed: 06/07/2023]
Abstract
We present a nonperturbative analysis of the power spectrum of energy level fluctuations in fully chaotic quantum structures. Focusing on systems with broken time-reversal symmetry, we employ a finite-N random matrix theory to derive an exact multidimensional integral representation of the power spectrum. The N→∞ limit of the exact solution furnishes the main result of this study-a universal, parameter-free prediction for the power spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power spectrum is merely determined by the spectral form factor of a quantum system.
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Affiliation(s)
- Roman Riser
- Department of Applied Mathematics, H.I.T.-Holon Institute of Technology, Holon 5810201, Israel
| | - Vladimir Al Osipov
- Division of Chemical Physics, Lund University, Getingevägen 60, Lund 22241, Sweden
| | - Eugene Kanzieper
- Department of Applied Mathematics, H.I.T.-Holon Institute of Technology, Holon 5810201, Israel
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36
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Dietz B, Yunko V, Białous M, Bauch S, Ławniczak M, Sirko L. Nonuniversality in the spectral properties of time-reversal-invariant microwave networks and quantum graphs. Phys Rev E 2017; 95:052202. [PMID: 28618543 DOI: 10.1103/physreve.95.052202] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2017] [Indexed: 11/06/2022]
Abstract
We present experimental and numerical results for the long-range fluctuation properties in the spectra of quantum graphs with chaotic classical dynamics and preserved time-reversal invariance. Such systems are generally believed to provide an ideal basis for the experimental study of problems originating from the field of quantum chaos and random matrix theory. Our objective is to demonstrate that this is true only for short-range fluctuation properties in the spectra, whereas the observation of deviations in the long-range fluctuations is typical for quantum graphs. This may be attributed to the unavoidable occurrence of short periodic orbits, which explore only the individual bonds forming a graph and thus do not sense the chaoticity of its dynamics. In order to corroborate our supposition, we performed numerous experimental and corresponding numerical studies of long-range fluctuations in terms of the number variance and the power spectrum. Furthermore, we evaluated length spectra and compared them to semiclassical ones obtained from the exact trace formula for quantum graphs.
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Affiliation(s)
- Barbara Dietz
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
| | - Vitalii Yunko
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
| | - Małgorzata Białous
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
| | - Szymon Bauch
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
| | - Michał Ławniczak
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
| | - Leszek Sirko
- Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
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37
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Li H, Suwunnarat S, Fleischmann R, Schanz H, Kottos T. Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers. PHYSICAL REVIEW LETTERS 2017; 118:044101. [PMID: 28186818 DOI: 10.1103/physrevlett.118.044101] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2016] [Indexed: 06/06/2023]
Abstract
We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γ_{CPA} and energy E_{CPA}, for which a CPA occurs, are expressed in terms of the eigenmodes of the isolated cavity-thus carrying over the information about the chaotic nature of the target-and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities.
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Affiliation(s)
- Huanan Li
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Suwun Suwunnarat
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Ragnar Fleischmann
- Max Planck Institute for Dynamics and Self-organization (MPIDS), 37077 Göttingen, Germany
| | - Holger Schanz
- Institute for Mechanical Engineering, Hochschule Magdeburg-Stendal, 39114 Magdeburg, Germany
| | - Tsampikos Kottos
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
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