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Leszek Sirko - One of the best experts on this subject based on the ideXlab platform.
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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
Physical Review E, 2020Co-Authors: Michal ławniczak, Bart Van Tiggelen, Leszek SirkoAbstract: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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investigation of the diagonal elements of the wigner s reaction matrix for networks with violated time reversal Invariance
Scientific Reports, 2019Co-Authors: Michal ławniczak, Leszek SirkoAbstract:The distributions of the diagonal elements of the Wigner's reaction [Formula: see text] 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 [Formula: see text] matrix were experimentally evaluated by measuring of the two-port scattering matrix [Formula: see text]. The violation of T Invariance in the networks with large absorption was demonstrated by calculating the enhancement factor W of the matrix [Formula: see text]. 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 [Formula: see text] 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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nonuniversality in the spectral properties of time reversal invariant microwave networks and quantum graphs
Physical Review E, 2017Co-Authors: Barbara Dietz, Malgorzata Bialous, Vitalii Yunko, Szymon Bauch, Michal ławniczak, Leszek SirkoAbstract: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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power spectrum analysis and missing level statistics of microwave graphs with violated time reversal Invariance
Physical Review Letters, 2016Co-Authors: Malgorzata Bialous, Barbara Dietz, Vitalii Yunko, Szymon Bauch, Michal ławniczak, Leszek SirkoAbstract:We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal Invariance. On the basis of our data sets, we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a procedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.g., nuclei or molecules, where one has to deal with the problem of missing levels.
Franziska Schäfer - One of the best experts on this subject based on the ideXlab platform.
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scattering experiments with microwave billiards at an exceptional point under broken time reversal Invariance
Physical Review E, 2014Co-Authors: S. Bittner, H. L. Harney, A Richter, B Dietz, M Miskioglu, Franziska SchäferAbstract:Scattering experiments with microwave cavities were performed and the effects of broken Time-Reversal Invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.
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Scattering experiments with microwave billiards at an exceptional point under broken Time-Reversal Invariance
Physical Review E - Statistical Nonlinear and Soft Matter Physics, 2014Co-Authors: S. Bittner, H. L. Harney, M. Miski-oglu, Barbara Dietz, A Richter, Franziska SchäferAbstract:Scattering experiments with microwave cavities were performed and the effects of broken Time-Reversal Invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found to be PT invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.
A Richter - One of the best experts on this subject based on the ideXlab platform.
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scattering experiments with microwave billiards at an exceptional point under broken time reversal Invariance
Physical Review E, 2014Co-Authors: S. Bittner, H. L. Harney, A Richter, B Dietz, M Miskioglu, Franziska SchäferAbstract:Scattering experiments with microwave cavities were performed and the effects of broken Time-Reversal Invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.
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Spectral properties and dynamical tunneling in constant-width billiards
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2014Co-Authors: BERND DIETZ, M. Miski-oglu, Barbara Dietz, Thomas Guhr, Boris Gutkin, A RichterAbstract:We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave resonators. While the classical dynamics of the constant-width billiards is unidirectional, a change of the direction of motion is possible in the corresponding quantum system via dynamical tunneling. This becomes manifest in a splitting of the vast majority of resonances into doublets of nearly degenerate ones. The fluctuation properties of the two respective spectra are demonstrated to coincide with those of a random-matrix model for systems with violated Time-Reversal Invariance and a mixed dynamics. Furthermore, we investigate tunneling in terms of the splittings of the doublet partners. On the basis of the random-matrix model we derive an analytical expression for the splitting distribution which is generally applicable to systems exhibiting dynamical tunneling between two regions with (predominantly) chaotic dynamics.
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Scattering experiments with microwave billiards at an exceptional point under broken Time-Reversal Invariance
Physical Review E - Statistical Nonlinear and Soft Matter Physics, 2014Co-Authors: S. Bittner, H. L. Harney, M. Miski-oglu, Barbara Dietz, A Richter, Franziska SchäferAbstract:Scattering experiments with microwave cavities were performed and the effects of broken Time-Reversal Invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found to be PT invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.
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Random matrices and chaos in nuclear physics: Nuclear reactions
Reviews of Modern Physics, 2010Co-Authors: G. E. Mitchell, A Richter, H A WeidenmullerAbstract:The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The implementation of a random-matrix approach into scattering theory leads to a statistical theory of CN reactions. Since RMT applies generically to chaotic quantum systems, that theory is, at the same time, a generic theory of quantum chaotic scattering. It uses a minimum of input parameters (average S-matrix and mean level spacing of the CN). Predictions of the theory are derived with the help of field-theoretical methods adapted from condensed-matter physics and compared with those of phenomenological approaches. Thorough tests of the theory are reviewed, as are applications in nuclear physics, with special attention given to violation of symmetries (isospin, parity) and Time-Reversal Invariance.
Yan V Fyodorov - One of the best experts on this subject based on the ideXlab platform.
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chaotic scattering with localized losses s matrix zeros and reflection time difference for systems with broken time reversal Invariance
Physical Review E, 2020Co-Authors: Mohammed Osman, Yan V FyodorovAbstract: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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statistics of off diagonal entries of wigner k matrix for chaotic wave systems with absorption
International Conference on Electromagnetics in Advanced Applications, 2019Co-Authors: Sirio Belga Fedeli, Yan V FyodorovAbstract:The phenomenon of chaotic resonance scattering of quantum waves has been the object of considerable theoretical and experimental investigations for the last three decades. In literature, most of the available results regarding the theoretical description of scattering characteristics strongly rely on the assumption of absence of absorption. At present few theoretical results for the associated distributions are available in the literature for the most interesting and experimentally relevant case of systems with preserved Time-Reversal Invariance. In addition, experimentally measured quantities are inevitably affected by energy losses, e.g. due to damping in resonator walls, imperfections and impurities. Following the ‘Heidelberg approach’, in this talk [1] we derive a random matrix formulation of the characteristic function for the off diagonal entries of the Wigner reaction matrix, K, i.e. the Cayley transform of the scattering matrix. In this framework we ‘substitute’ the Hamiltonian operator H with ensembles of random matrices used to model the chaotic system. Therefore, the losses mentioned above, in the case of uniform absorption, can be introduced in the model by introducing an imaginary component for the spectral energy parameter: $\lambda\rightarrow\lambda+\mathrm{i}\ \alpha/\mathrm{N}$ . This replacement breaks the Hermiticity of K while the scattering matrix is no longer unitary. Rescaling with the size of the system, N, allows to investigate regimes for which the absorption is of the same order of magnitude of the mean separation between neighboring eigenvalues of the wave-chaotic Hamiltonian H. As benchmark and preliminary study, we firstly consider systems with broken time reversal Invariance and we extend previous results contained in [2]. Secondly, we derive non-trivial statistics for the off diagonal terms of K for system with preserved time reversal Invariance associated to the Gaussian Orthogonal Ensemble. In this case the full access to the bulk regime is guaranteed by the spectral universality of the ensemble.
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statistics of off diagonal entries of wigner k matrix for chaotic wave systems with absorption
arXiv: Statistical Mechanics, 2019Co-Authors: Sirio Belga Fedeli, Yan V FyodorovAbstract:Using the Random Matrix Theory approach we derive explicit distributions of the real and imaginary parts for off-diagonal entries of the Wigner reaction matrix $\mathbf{K}$ for wave chaotic scattering in systems with and without Time-Reversal Invariance, in the presence of an arbitrary uniform absorption.
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statistics of resonance poles phase shifts and time delays in quantum chaotic scattering random matrix approach for systems with broken time reversal Invariance
Journal of Mathematical Physics, 1997Co-Authors: Yan V Fyodorov, Hansjurgen SommersAbstract:Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first part of the paper we attempt to expose systematically ideas underlying the so-called stochastic (Heidelberg) approach to chaotic quantum scattering. Then we concentrate on systems with broken Time-Reversal Invariance coupled to continua via Mopen channels; a=1,2,…,M. A physical realization of this case corresponds to the chaotic scattering in ballistic microstructures pierced by a strong enough magnetic flux. By using the supersymmetry method we derive an explicit expression for the density of S-matrix poles (resonances) in the complex energy plane. When all scattering channels are considered to be equivalent our expression describes a crossover from the χ2 distribution of resonance widths (regime of isolated resonances) to a broad power-like distribution typical for the regime of overlapping resonances. The first moment is found to reproduce exactly the Moldauer–Simonius relation between the mean resonance width and the transmission coefficient. Under the same assumptions we derive an explicit expression for the parametric correlation function of densities of eigenphases θa of the S-matrix (taken modulo 2π). We use it to find the distribution of derivatives τa=∂θa/∂E of these eigenphases with respect to the energy (“partial delay times”) as well as with respect to an arbitrary external parameter. We also find the parametric correlations of the Wigner–Smith time delay τw(E)=(1/M)∑a ∂θa/∂E at two different energies E−Ω/2 and E+Ω/2 as well as at two different values of the external parameter. The relation between our results and those following from the semiclassical approach as well as the relevance to experiments are briefly discussed.
Barbara Dietz - One of the best experts on this subject based on the ideXlab platform.
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nonuniversality in the spectral properties of time reversal invariant microwave networks and quantum graphs
Physical Review E, 2017Co-Authors: Barbara Dietz, Malgorzata Bialous, Vitalii Yunko, Szymon Bauch, Michal ławniczak, Leszek SirkoAbstract: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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power spectrum analysis and missing level statistics of microwave graphs with violated time reversal Invariance
Physical Review Letters, 2016Co-Authors: Malgorzata Bialous, Barbara Dietz, Vitalii Yunko, Szymon Bauch, Michal ławniczak, Leszek SirkoAbstract:We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal Invariance. On the basis of our data sets, we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a procedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.g., nuclei or molecules, where one has to deal with the problem of missing levels.
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Spectral properties and dynamical tunneling in constant-width billiards
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2014Co-Authors: BERND DIETZ, M. Miski-oglu, Barbara Dietz, Thomas Guhr, Boris Gutkin, A RichterAbstract:We determine with unprecedented accuracy the lowest 900 eigenvalues of two quantum constant-width billiards from resonance spectra measured with flat, superconducting microwave resonators. While the classical dynamics of the constant-width billiards is unidirectional, a change of the direction of motion is possible in the corresponding quantum system via dynamical tunneling. This becomes manifest in a splitting of the vast majority of resonances into doublets of nearly degenerate ones. The fluctuation properties of the two respective spectra are demonstrated to coincide with those of a random-matrix model for systems with violated Time-Reversal Invariance and a mixed dynamics. Furthermore, we investigate tunneling in terms of the splittings of the doublet partners. On the basis of the random-matrix model we derive an analytical expression for the splitting distribution which is generally applicable to systems exhibiting dynamical tunneling between two regions with (predominantly) chaotic dynamics.
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Scattering experiments with microwave billiards at an exceptional point under broken Time-Reversal Invariance
Physical Review E - Statistical Nonlinear and Soft Matter Physics, 2014Co-Authors: S. Bittner, H. L. Harney, M. Miski-oglu, Barbara Dietz, A Richter, Franziska SchäferAbstract:Scattering experiments with microwave cavities were performed and the effects of broken Time-Reversal Invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found to be PT invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.
