Chaotic scattering in the regime of weakly overlapping resonances

Dietz, Barbara; Friedrich, Thomas; Harney, H. L.; Miski-Oglu, Maksym; Richter, A.; Schäfer, F.; Weidenmüller, H. A.

doi:10.1103/physreve.78.055204

Cited by 31 publications

(43 citation statements)

References 20 publications

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“…For their experimental verification, scattering data were taken at room temperature using a microwave resonator with the shape of a chaotic tilted stadium billiard allowing tests also with unprecedented accuracy in the regions of isolated and weakly overlapping resonances. 34,[36][37][38][39] Experiments were furthermore performed with microwave billiards where a partial T violation was induced by a magnetized ferrite. 40 For the analysis of the latter, we extended predictions derived for T -invariant systems by Verbaarschot, Weidenm€ uller, and Zirnbauer 32 for the Smatrix autocorrelation functions to systems with partial T violation.…”

Section: Quantum Chaos In Closed and Open Systems: The Bunimovicmentioning

confidence: 99%

Quantum and wave dynamical chaos in superconducting microwave billiards

Dietz

Richter

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose of the present article is to recapitulate some of the highlights achieved. We briefly review (i) results obtained with flat, cylindrical microwave resonators, so-called microwave billiards, concerning the universal fluctuation properties of the eigenvalues of classically chaotic systems with no, a threefold and a broken symmetry; (ii) summarize our findings concerning the wave-dynamical chaos in three-dimensional microwave cavities; (iii) present a new approach for the understanding of the phenomenon of dynamical tunneling which was developed on the basis of experiments that were performed recently with unprecedented precision, and finally, (iv) give an insight into an ongoing project, where we investigate universal properties of (artificial) graphene with superconducting microwave photonic crystals that are enclosed in a microwave resonator, i.e., so-called Dirac billiards.

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Section: Quantum Chaos In Closed and Open Systems: The Bunimovicmentioning

confidence: 99%

Quantum and wave dynamical chaos in superconducting microwave billiards

Dietz

Richter

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…It is to be noticed that for α = ∞ we retrieve the case where ports/apertures radiate in free-space. In the limit of infinitesimal losses the impedance fluctuation become very strong: this is a situation that can occur in superconducting cavities Alt et al (1998), in low-loss optical systems, e.g., lasers Türeci et al (2006), in microwave cavities operated in the non-Ericsson (weak overlapping) regime Dietz et al (2008Dietz et al ( , 2009, and in reverberation chambers/enclosures operated in the undermoded regime Arnaut (2001); Warne et al (2003); Orjubin et al (2006); Arnaut and Gradoni (2011).…”

Section: Random Coupling Model In Action: Numerical Simulationsmentioning

confidence: 99%

Predicting the statistics of wave transport through chaotic cavities by the random coupling model: A review and recent progress

et al. 2014

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In this review, a model (the Random Coupling Model) that gives a statistical description of the coupling of radiation into and out of large enclosures through localized and/or distributed channels is presented. The Random Coupling Model combines both deterministic and statistical phenomena. The model makes use of wave chaos theory to extend the classical modal description of the cavity fields in the presence of boundaries that lead to chaotic ray trajectories. The model is based on a clear separation between the universal statistical behavior of the isolated chaotic system, and the deterministic coupling channel characteristics. Moreover, the ability of the random coupling model to describe interconnected cavities, aperture coupling, and the effects of short ray trajectories is discussed. A relation between the random coupling model and other formulations adopted in acoustics, optics, and statistical electromagnetics, is examined. In particular, a rigorous analogy of the random coupling model with the Statistical Energy Analysis used in acoustics is presented.

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“…3(b). The shape of the cavity is a symmetry-reduced "cut-circle" that shows chaos for ray trajectories [24,[50][51][52][53]. The superconducting cavity is made of copper with Pb-plated walls and cooled to a temperature (6.6 [K]) below the transition temperature of Pb.…”

Section: A Three Experimental Systemsmentioning

confidence: 99%

Impedance and Scattering Variance Ratios of Complicated Wave Scattering Systems in the Low Loss Regime

et al. 2013

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Random matrix theory successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model oers a complete statistical model with a simple additive formula in terms of impedance to combine the predictions of random matrix theory and nonuniversal system-specic features. The statistics of measured wave properties generally have nonuniversal features. However, ratios of the variances of elements of the impedance matrix are predicted to be independent of such nonuniversal features and thus should be universal functions of the overall system loss. In contrast with impedance variance ratios, scattering variance ratios depend on nonuniversal features unless the system is in the high loss regime. In this paper, we present numerical tests of the predicted universal impedance variance ratios and show that an insucient sample size can lead to apparent deviation from the theory, particularly in the low loss regime. Experimental tests are carried out in three two-port microwave cavities with varied loss parameters, including a novel experimental system with a superconducting microwave billiard, to test the variance-ratio predictions in the low loss time-reversal-invariant regime. It is found that the experimental results agree with the theoretical predictions to the extent permitted by the nite sample size.

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Chaotic scattering in the regime of weakly overlapping resonances

Cited by 31 publications

References 20 publications

Quantum and wave dynamical chaos in superconducting microwave billiards

Quantum and wave dynamical chaos in superconducting microwave billiards

Predicting the statistics of wave transport through chaotic cavities by the random coupling model: A review and recent progress

Impedance and Scattering Variance Ratios of Complicated Wave Scattering Systems in the Low Loss Regime

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