Microwave study of quantum<b><i>n</i></b>-disk scattering

Lu, W. T.; Viola, Lorenza; Pance, Kristi; Rose, Michael; Sridhar, S.

doi:10.1103/physreve.61.3652

Cited by 22 publications

(24 citation statements)

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“…In our experiments the coax lines act as tunneling point contacts, and hence it can be shown [9] that…”

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confidence: 99%

“…The above equation was used to fit the spectral autocorrelation for small κ and thus obtain the value of the experimental escape rate γ qm [8,9]. Good agreement of the escape rate is obtained between γ qm obtained from the experiments and γ cl of the classical theory [9]. For intermediate κ, the semiclassical prediction of Eq.…”

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confidence: 99%

“…Similar microwave experiments, which exploit this QM-E&M mapping, have been used to study quantum chaos in closed [13,14] and open systems [8]. See [9] for details of the experiments.…”

mentioning

confidence: 99%

“…1. See [9] for details of the comparison of the resonances between experiments and semiclassical calculations. The spectral autocorrelation function was calculated as [9] …”

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confidence: 99%

“…Because we ensure that the coupling to the leads is very weak, any shifts due to the leads are negligible (< 10 −4 of the resonance frequencies and widths) [9]. The n-disk systems are investigated in the fundamental domain [10], as shown in the inset to Fig.1, with angles 90 • (n = 2), 60 • (n = 3), and 45 • (n = 4).…”

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confidence: 99%

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Quantum Fingerprints of Classical Ruelle-Pollicott Resonances

Pance

Sridhar

2000

Phys. Rev. Lett.

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N-disk microwave billiards, which are representative of open quantum systems, are studied experimentally. The transmission spectrum yields the quantum resonances which are consistent with semiclassical calculations. The spectral autocorrelation of the quantum spectrum is shown to be determined by the classical Ruelle-Pollicot resonances, arising from the complex eigenvalues of the Perron-Frobenius operator. This work establishes a fundamental connection between quantum and classical correlations in open systems.The quantum-classical correspondence for chaotic systems has been studied extensively in the context of universality and periodic orbit contributions. This approach has focussed on eigenvalues and eigenfunctions and their statistical properties. Universality has been shown to arise from Random Matrix Theory [1], while periodic orbit contributions have been analyzed in the semiclassical scheme for calculations of eigenvalue spectra [2] and constructions of eigenfunctions [3].An entirely different approach is to consider correlations of observables. In the classical context a probabilistic approach is best taken with Liouvillian dynamics. In certain classical systems these have been shown to lead to Ruelle-Pollicot (RP) resonances [4,5], arising from complex eigenvalues of the Perron-Frobenius operator. In open systems, this leads to a quantitative description of the timeevolution of classical observables, the most common being the particle density. In the quantum context, diffusive transport has been argued to be intimately connected with Liouvillian dynamics, not just in disordered systems where the correspondence is made with nonlinear σ−models of supersymmetry [6] but also in individual chaotic systems which represent a ballistic limit.In this paper we present a microwave experiment which demonstrates this deep connection between quantum properties and classical diffusion. Our experiment is a microwave realization of the wellknown n-disk geometry, which is a paradigm of an open quantum chaotic system, along with other systems such as the Smale horseshoe and the Baker map [7]. The classical scattering function of the chaotic n-disk system is nondifferentiable and has a selfsimilar fractal structure. A central property is the exponential decay of an initial distribution of classical particles, due to the unstable periodic orbits, which form a cantor set, hence the name fractal repeller. The experimental transmission spectrum directly yields the frequencies and the widths of the low lying quantum resonances of the system [8,9], which are in agreement with semiclassical periodic orbit calculations [10,11,12]. The same spectra are analyzed to obtain the spectral wave-vector autocorrelation C(κ) [8]. The wave vector dependence of the spectral autocorrelation is shown to be completely described by the leading RP resonances of the corresponding classical system. The small κ (long time) behavior of the spectral autocorrelation provides a measure of the quantum escape rate, and is shown to be in good agr...

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“…In our experiments the coax lines act as tunneling point contacts, and hence it can be shown [9] that…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…Similar microwave experiments, which exploit this QM-E&M mapping, have been used to study quantum chaos in closed [13,14] and open systems [8]. See [9] for details of the experiments.…”

mentioning

confidence: 99%

“…1. See [9] for details of the comparison of the resonances between experiments and semiclassical calculations. The spectral autocorrelation function was calculated as [9] …”

mentioning

confidence: 99%

mentioning

confidence: 99%

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