Experimental Determination of the Autocorrelation Function of Level Velocities for Microwave Networks Simulating Quantum Graphs

Ławniczak, Michał; Borkowska, A.; Hul, Oleh; Bauch, Szymon; Sirko, Leszek

doi:10.12693/aphyspola.120.a-185

Cited by 7 publications

(4 citation statements)

References 48 publications

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“…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%

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: Introductionmentioning

confidence: 99%

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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“…In this way one obtains an ensemble of random states associated to a graph Γ, which can be considered as a generalization of the ensembles investigated in [3,4]. On the other hand the above construction of an ensemble of quantum states corresponding to a graph differs from the notion of quantum graphs studied by Gnutzmann and Smilansky [22] or these related to microwave experiments investigated in [23,24].…”

Section: Discussionmentioning

confidence: 98%

Random Unitary Matrices Associated to a Graph

Kondratiuk

Życzkowski

2013

Acta Phys. Pol. A

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We analyze composed quantum systems consisting of k subsystems, each described by states in the n-dimensional Hilbert space. Interaction between subsystems can be represented by a graph, with vertices corresponding to individual subsystems and edges denoting a generic interaction, modeled by random unitary matrices of order n 2 . The global evolution operator is represented by a unitary matrix of size N = n k . We investigate statistical properties of such matrices and show that they display spectral properties characteristic to the Haar random unitary matrices provided the corresponding graph is connected. Thus basing on random unitary matrices of a small size n 2 one can construct a fair approximation of large random unitary matrices of size n k . Graph-structured random unitary matrices investigated here allow one to dene the corresponding structured ensembles of random pure states.

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“…33 GHz [74], where c is the speed of light in vacuum. Absorption of the networks can be controlled by changing their length and/or by introducing to them microwave attenuators [59,60]. In these measurements fifteen 2 dB attenuators, one at each bond, were introduced.…”

Section: Methodsmentioning

confidence: 99%

“…It is worth noting that the imaginary part (v > 0) of the Wigner reaction matrix K ≡ u − i v is known in solid-state physics as the local density of states (LDoS) [55]. Experimentally the Wigner reaction matrix K was investigated in microwave cavities [35,57,58] and for moderate and (811) strong losses γ ≤ 47.7 in microwave networks [20,[59][60][61]. Quantum networks with leads are very interesting open systems and therefore they were also thoroughly studied theoretically [14,19,21,62].…”

Section: Properties Of Trs Invariant Open Systems (β = 1)mentioning

confidence: 99%

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

et al. 2019

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

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Experimental Determination of the Autocorrelation Function of Level Velocities for Microwave Networks Simulating Quantum Graphs

Cited by 7 publications

References 48 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

Random Unitary Matrices Associated to a Graph

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

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