Power spectrum of nuclear spectra with missing levels and mixed symmetries

Molina, Rafael A.; Retamosa, J.; Muñoz, L.; Relaño, Armando; Faleiro, E.

doi:10.1016/j.physletb.2006.10.058

Cited by 38 publications

(48 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It was demonstrated numerically in Ref. [44] that the power spectrum [45,46] is a powerful statistical measure to discriminate between deviations caused by missing levels and by the mixing of symmetries. Additional evidence for these effects may be obtained on the basis of commonly used statistical measures for short-and longrange spectral fluctuations [43].…”

Section: Arxiv:160906073v1 [Nlincd] 20 Sep 2016mentioning

confidence: 99%

“…3 and 4 indeed are solely due to missing levels we analysed power spectra. An analytical expression was derived for the power spectrum of incomplete spectra in Ref [44],…”

Section: Figmentioning

confidence: 99%

“…(5) for the power spectrum given in Ref. [44]. All these expressions explicitly take into account the fraction of observed levels ϕ, however, the power spectrum is particularly sensitive to it.…”

Section: Figmentioning

confidence: 99%

See 2 more Smart Citations

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

et al. 2016

View full text Add to dashboard Cite

We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal invariance. On the basis of our data sets we demonstrate that the power spectrum in combination with other long-range and also short-range spectral fluctuations provides a powerful tool for the identification of the symmetries and the determination of the fraction of missing levels. Such a procedure is indispensable for the evaluation of the fluctuation properties in the spectra of real physical systems like, e.g., nuclei or molecules, where one has to deal with the problem of missing levels. Introduction.-In the last decades the concept of quantum chaos, that is, the understanding of the features of the classical dynamics in terms of the spectral properties of the corresponding quantum system, like nuclei, atoms, molecules, quantum wires and dots or other complex systems [1][2][3], has been elaborated extensively. It has been established by now that the spectral properties of generic quantum systems with classically regular dynamics agree with those of Poissonian random numbers [4] while they coincide with those of the eigenvalues of random matrices [6] from the Gaussian orthogonal ensemble (GOE) and the Gaussian unitary ensemble (GUE) for classically chaotic systems with and without timereversal (T ) invariance [5], respectively, in accordance with the Bohigas-Giannoni-Schmit (BGS) conjecture [7].A multitude of studies with focus on problems from the field of quantum chaos have been performed by now theoretically and numerically. However, there are nongeneric features in the spectra of real physical systems that are not yet fully understood. Such problems are best tackled experimentally with the help of model systems like microwave billiards [8,9] and microwave graphs [10,11]. In the experiments with microwave billiards the analogy between the scalar Helmholtz equation and the Schrödinger equation of the corresponding quantum billiard is exploited. Microwave graphs [10,11] simulate the spectral properties of quantum graphs [12][13][14], networks of onedimensional wires joined at vertices. They provide an extremely rich system for the experimental and the theoretical study of quantum systems, that exhibit a chaotic dynamics in the classical limit.The idea of quantum graphs was introduced by Linus Pauling to model organic molecules [15] and they are also used to simulate, e.g., quantum wires [16], optical waveguides [17] and mesoscopic quantum systems [18,19]. The validity of the BGS conjecture was proven rigourously for graphs with incommensurable bond lengths in Refs. [20,21]. Accordingly, the fluctuation properties in the spectra of classically chaotic quantum graphs with and without T invariance are expected

show abstract

Section: Arxiv:160906073v1 [Nlincd] 20 Sep 2016mentioning

confidence: 99%

“…3 and 4 indeed are solely due to missing levels we analysed power spectra. An analytical expression was derived for the power spectrum of incomplete spectra in Ref [44],…”

Section: Figmentioning

confidence: 99%

See 1 more Smart Citation

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

et al. 2016

View full text Add to dashboard Cite

show abstract

“…1) we can obtain the energy time series of the fluctuations. In [10,11] the method of power spectrum analysis (PS) [14,15,16,17] is used to study the statistical of fluctuations of energy time series. Following the 1/f β noise convention, three of the most conventional noises present in nature are for β = 2, 1, 0 corresponding to thermal (Brownian), chaotic and Poisson noise respectively [12].…”

Section: Power Spectrum and Visibilitymentioning

confidence: 99%

Quantum interference vs. quantum chaos in the nuclear shell model

Fernández

Hernández

Hautefeuille

et al. 2015

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract. In this paper we study the complexity of the nuclear states in terms of a two body quadupole-quadrupole interaction. Energy distributions and eigenvectors composition exhibit a visible interference pattern which is dependent on the intensity of the interaction. In analogy with optics, the visibility of the interference is related to the purity of the states, therefore, we show that the fluctuations associated with quantum chaos have as their origin the remaining quantum coherence with a visibility magnitude close to 5%.

show abstract

“…al. demonstrated numerically [55] that the power spectrum [56][57][58][59][60] is a powerful statistical measure to discriminate between deviations caused by missing levels and by the mixing of symmetries. Additional information on missing levels may be obtained on the basis of commonly used statistical measures for short-and longrange spectral fluctuations [54].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Missing Level Statistics for Microwave Networks Simulating Quantum Chaotic Graphs Without Time Reversal Symmetry - the Case of Randomly Lost Resonances

et al. 2017

View full text Add to dashboard Cite

We present experimental and numerical studies for level statistics in incomplete spectra obtained with microwave networks simulating quantum chaotic graphs with broken time reversal symmetry. We demonstrate that, if resonance frequencies are randomly removed from the spectra, the experimental results for the nearest-neighbor spacing distribution, the spectral rigidity and the average power spectrum are in good agreement with theoretical predictions for incomplete sequences of levels of systems with broken time reversal symmetry.

show abstract

Power spectrum of nuclear spectra with missing levels and mixed symmetries

Cited by 38 publications

References 24 publications

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

Power Spectrum Analysis and Missing Level Statistics of Microwave Graphs with Violated Time Reversal Invariance

Quantum interference vs. quantum chaos in the nuclear shell model

Analysis of Missing Level Statistics for Microwave Networks Simulating Quantum Chaotic Graphs Without Time Reversal Symmetry - the Case of Randomly Lost Resonances

Contact Info

Product

Resources

About