Experimental and numerical determination of the correlation function of level velocities for microwave networks simulating quantum graphs

Ławniczak, Michał; Nicolau-Kuklińska, Agata; Hul, Oleh; Masiak, Paweł; Bauch, Szymon; Sirko, Leszek

doi:10.1088/0031-8949/2013/t153/014041

Cited by 3 publications

(4 citation statements)

References 49 publications

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“…For each realization of a microwave graph the absorption strength was evaluated by fitting the theoretical mean reflection coefficientto the experimental one obtained after eliminating the direct processes 36,37,43 . Here the index i = 1, 2 denotes the port 1 or 2.…”

Section: Resultsmentioning

confidence: 99%

“…The distributions P ( ʋ ) and P ( u ) of the imaginary and the real parts of the Wigner’s reaction matrix as well as the reflection coefficient P ( R ) were theoretically investigated for all ranges of the dimensionless parameter γ = 2 π Γ/Δ, characterizing the absorption strength 38,39 , where Γ and Δ are the width of resonances and the mean level spacing, respectively. For microwave chaotic cavities they were experimentally studied in refs 40–42 and for microwave graphs, in the case of medium and large absorption strength γ ≤ 47.7, they were investigated in refs 17,43–45 . It is important to point out that the distribution of the imaginary P ( ʋ ) parts of the diagonal elements of the Wigner’s reaction matrix is known in solid-state physics as the local density of states (LDoS) 38 .…”

Section: Introductionmentioning

confidence: 99%

“…For the SMA-RG402 coaxial cable the TE 11 mode cut-off frequency is GHz 54 , where c is the speed of light in vacuum. Absorption of the networks was effectively controlled by adding to the networks microwave attenuators 1 dB and 2 dB, respectively 43,44 .…”

Section: Introductionmentioning

confidence: 99%

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

Ławniczak

Sirko

2019

Sci Rep

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

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ławniczak

Sirko

2019

Sci Rep

Self Cite

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“…As typical for quantum chaos, those experiments were not carried out on eigenvalues of the Schrödinger equation, but rather on related models of quasi-2D microwave cavities or propagation of acoustic waves. We provide an incomplete list of references to beautiful experiments [ 18 , 19 , 20 , 21 , 22 , 23 , 24 ] stressing the work of the Stöckmann group [ 18 ] where a rather complete comparison of different measures with experimental microwave resonance data was carried out.…”

Section: Introductionmentioning

confidence: 99%

Quantum Chaos and Level Dynamics

Zakrzewski

2023

Entropy

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We review the application of level dynamics to spectra of quantally chaotic systems. We show that the statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics, such as level avoided-crossing distributions, level slope distributions, or level curvature distributions. We show both the aspects of universality in these distributions and their limitations. We concentrate in some detail on measures imported from the quantum information approach such as the fidelity susceptibility, and more generally, geometric tensor matrix elements. The possible open problems are suggested.

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Experimental and numerical investigation of parametric spectral properties of quantum graphs with unitary or symplectic symmetry

Che

Zhang

et al. 2020

Phys. Rev. E

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Experimental and numerical determination of the correlation function of level velocities for microwave networks simulating quantum graphs

Cited by 3 publications

References 49 publications

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

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

Quantum Chaos and Level Dynamics

Experimental and numerical investigation of parametric spectral properties of quantum graphs with unitary or symplectic symmetry

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