Distribution of eigenmodes in a superconducting stadium billiard with chaotic dynamics

Gräf, H.‐D.; Harney, H. L.; Lengeler, H.; Lewenkopf, Caio; Rangacharyulu, C.; Richter, A.; Schardt, P.; Weidenmüller, Hans A.

doi:10.1103/physrevlett.69.1296

Cited by 261 publications

(204 citation statements)

References 17 publications

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“…One class of these "quantum" billiards are the Bunimovich stadium billiards [8] experimentally investigated in Refs. [1,7,[9][10][11][12].…”

Section: The Experiments With Coupled Microwave Resonatorsmentioning

confidence: 99%

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Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference

Barbosa

Harney

2000

Phys. Rev. E

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Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes of levels. The number variance is used to quantify the level fluctuations as a function of the coupling and to construct the conditional probability distribution of the data. The prior distribution of the coupling parameter is obtained from an invariance argument on the entropy of the posterior distribution.

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“…One class of these "quantum" billiards are the Bunimovich stadium billiards [8] experimentally investigated in Refs. [1,7,[9][10][11][12].…”

Section: The Experiments With Coupled Microwave Resonatorsmentioning

confidence: 99%

“…They have been studied extensively, see the review article [3]. Quantum mechanical billiards can be simulated by flat microwave resonators [4][5][6][7]. One class of these "quantum" billiards are the Bunimovich stadium billiards [8] experimentally investigated in Refs.…”

Section: The Experiments With Coupled Microwave Resonatorsmentioning

confidence: 99%

Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference

Barbosa

Harney

2000

Phys. Rev. E

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“…In scattering systems similar matters have been discussed mainly for systems that are chaotic and hyperbolic [12,29], or mixed [30,31,32,33,34]. The role of parabolic manifolds has also received considerable attention [7,35].…”

Section: Introductionmentioning

confidence: 99%

“…In physics they have acquired increasing importance as they are seen to emulate properties of systems as different as quantum dots [2] or planetary rings [3]. Particularly quantum or wave realizations of such objects have become popular, since flat microwave cavities, socalled microwave billiards, are used by experimentalists at different laboratories [4,5,6,7,8,9,10], and these experiments mimic some properties of mesoscopic devices. From a mathematical point of view one of the advantages of billiards is that, in many instances, chaotic properties can be proven for cases of complete chaos [1,11,12,13] and more recently even for mixed systems [14,15].…”

Section: Introductionmentioning

confidence: 99%

Nonperiodic echoes from mushroom billiard hats

et al. 2006

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Mushroom billiards have the remarkable property to show one or more clear cut integrable islands in one or several chaotic seas, without any fractal boundaries. The islands correspond to orbits confined to the hats of the mushrooms, which they share with the chaotic orbits. It is thus interesting to ask how long a chaotic orbit will remain in the hat before returning to the stem. This question is equivalent to the inquiry about delay times for scattering from the hat of the mushroom into an opening where the stem should be. For fixed angular momentum we find that no more than three different delay times are possible. This induces striking nonperiodic structures in the delay times that may be of importance for mesoscopic devices and should be accessible to microwave experiments.

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“…To illustrate how it works, we are going then to apply it to the case of a flat microwave cavity to which a thin antenna is attached. We compute the resonance spacing distribution in this system and show that it reproduces experimental data -within certain range of energies but without introducing any free parameters.Many recent studies involve an analysis, both theoretical and experimental, of spectral and transport properties of systems with a complicated geometry: let us recall various microwave resonators [1,2,3,4,5] or conductance fluctuations in quantum dots -see [6,7,8,9] and references therein. …”

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confidence: 99%

Resonance statistics in a microwave cavity with a thin antenna

Exner

Šeba

1997

Physics Letters A

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We propose a model for scattering in a flat resonator with a thin antenna. The results are applied to rectangular microwave cavities. We compute the resonance spacing distribution and show that it agrees well with experimental data provided the antenna radius is much smaller than wavelengths of the resonance wavefunctions.The aim of the present letter is twofold. First of all, we want to present a method to treat scattering in systems consisting of components of different dimensionality. To illustrate how it works, we are going then to apply it to the case of a flat microwave cavity to which a thin antenna is attached. We compute the resonance spacing distribution in this system and show that it reproduces experimental data -within certain range of energies but without introducing any free parameters.Many recent studies involve an analysis, both theoretical and experimental, of spectral and transport properties of systems with a complicated geometry: let us recall various microwave resonators [1,2,3,4,5] or conductance fluctuations in quantum dots -see [6,7,8,9] and references therein.

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Distribution of eigenmodes in a superconducting stadium billiard with chaotic dynamics

Cited by 261 publications

References 17 publications

Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference

Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference

Nonperiodic echoes from mushroom billiard hats

Resonance statistics in a microwave cavity with a thin antenna

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