Nonperiodic echoes from quantum mushroom-billiard hats

Dietz, Barbara; Friedrich, Thomas; Miski-Oglu, Maksym; Richter, A.; Schäfer, F.; Seligman, T. H.

doi:10.1103/physreve.80.036212

Cited by 10 publications

(6 citation statements)

References 41 publications

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“…Pin,a = |S ba | 2 of the rf signal sent into the resonator at antenna a and coupled out at antenna b and thus the complex scattering matrix element S ba = |S ba |e iφ ba describing this scattering process [50][51][52]. In the vicinity of an isolated or weakly overlapping resonance at f = f n S ba is well described by the complex Breit-Wigner form…”

Section: Methodsmentioning

confidence: 99%

“…The scattering matrix formalism describing microwave resonators was shown to be identical with that for compoundnucleus reactions. [43,62] This analogy has been employed in the previous group of one of the authors (BD) in a sequence of experiments [50][51][52][63][64][65][66] to investigate the universal properties of the scattering matrix for compound-nucleus reactions and, generally, for quantum scattering processes with intrinsic chaotic dynamics, that is, to verify the analytical results derived on the basis of the supersymmetry and RMT approach.…”

Section: Spectral Fluctuation Properties and Wavefunctionsmentioning

confidence: 99%

“…The matrix elements W aµ and W bµ describe the couplings of the antenna modes to the resonator modes. Furthermore, absorption in the wall of the resonator is modeled [51,52] by Λ fictitious channels W cµ . In the microwave experiments, the frequency-averaged S-matrix was diagonal, S ba = S aa δ ba , 100502-8 that is, direct processes were negligible.…”

Section: Spectral Fluctuation Properties and Wavefunctionsmentioning

confidence: 99%

See 2 more Smart Citations

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards*

Zhang¹,

Zhang²,

Dietz³

et al. 2019

Chinese Phys. B

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We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes a transition from integrable via almost integrable to fully chaotic. To realize such a system we chose a billiard with a 60 • sector shape of which the classical dynamics is integrable, and introduced circular scatterers of varying number, size and position. The spectral properties of generic quantum systems of which the classical counterpart is either integrable or chaotic are universal and well understood. If, however, the classical dynamics is pseudo-integrable or almost-integrable, they exhibit a non-universal intermediate statistics, for which analytical results are known only in a few cases, like, e.g., if it corresponds to semi-Poisson statistics. Since the latter is, above all, clearly distinguishable from those of integrable and chaotic systems our aim was to design a billiard with these features which indeed is achievable by adding just one scatterer of appropriate size and position to the sector billiard. We demonstrate that, while the spectral properties of almostintegrable billiards are sensitive to the classical dynamics, this is not the case for the distribution of the wavefunction components, which was analysed in terms of the strength distribution, and the fluctuation properties of the scattering matrix which coincide with those of typical, fully chaotic systems.

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Section: Methodsmentioning

confidence: 99%

Section: Spectral Fluctuation Properties and Wavefunctionsmentioning

confidence: 99%

Section: Spectral Fluctuation Properties and Wavefunctionsmentioning

confidence: 99%

See 1 more Smart Citation

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards*

Zhang¹,

Zhang²,

Dietz³

et al. 2019

Chinese Phys. B

View full text Add to dashboard Cite

show abstract

“…The matrix elements of Ŵ are real, Gaussian distributed with W aµ and W bµ describing the coupling of the antenna channels to the resonator modes. Furthermore, we chose Λ equal fictituous channels to account for the Ohmic losses in the walls of the resonator [83,88]. Direct transmission between the antennas was negligible, so that the frequency-averaged S-matrix was diagonal, implying that N µ=1 W eµ W e µ = N v 2 e δ ee [89].…”

Section: S-matrix Fluctuationsmentioning

confidence: 99%

Properties of the eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry

Zhang¹,

Zhang²,

Che³

et al. 2023

Preprint

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We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational C3 symmetry. Its band structure exhibits two Dirac points (DPs) that are separated by a nearly flat band. We present a procedure which we employed to identify eigenfrequencies and to separate the eigenstates according to their transformation properties under rotation by 2π3 into the three C3 subspaces. This allows us to verify previous numerical results of Ref.[W. Zhang and B. Dietz, Phys. Rev. B 104, 064310 (2021)], thus confirming that the properties of the eigenmodes coincide with those of artificial graphene around the lower DP, and are well described by a tight-binding model (TBM) for a honeycomb-kagome lattice of corresponding shape. Above all, we investigate properties of the wave-function components in terms of the fluctuation properties of the measured scattering matrix, which are numerically not accessible. They are compared to random-matrix theory predictions for quantum-chaotic scattering systems exhibiting extended or localized states in the interaction region, that is, the DB. Even in regions, where the wave functions are localized, the spectral properties coincide with those of typical quantum systems with chaotic classical counterpart.

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“…This problem can be circumvented by restricting to statistical measures which do not rely on completeness. This is possible, e.g., in microwave billiards or microwave networks where scattering matrix elements are available whose fluctuation properties also provide measures for the chaoticity, e.g., in terms of their correlation functions, the distributions of their cross sections [66][67][68][69] or the enhancement factor [26,70,71]. Complete spectra were obtained in experiments with superconducting microwave billiards [72,73] by choosing ei-ther resonators made from niobium or from lead-covered brass.…”

Section: Introductionmentioning

confidence: 99%

Missing-level statistics in classically chaotic quantum systems with symplectic symmetry

Che,

Lu,

Zhang

et al. 2021

Preprint

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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 [O. Bohigas and M. P. Pato, Phys. Rev. E 74, 036212 (2006)] 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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Nonperiodic echoes from quantum mushroom-billiard hats

Cited by 10 publications

References 41 publications

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards*

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards*

Properties of the eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry

Missing-level statistics in classically chaotic quantum systems with symplectic symmetry

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