Random matrices and chaos in nuclear physics: Nuclear structure

Weidenmüller, H. A.; Mitchell, G. E.

doi:10.1103/revmodphys.81.539

Cited by 314 publications

(350 citation statements)

References 198 publications

(321 reference statements)

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“…Although there have been several other successful tests of RMT using nuclear resonances, the NDE is perhaps the most important because, as stated in Ref. [2], "As a result of these analyses, it became generally accepted that proton and neutron resonances in medium weight and heavy nuclei agree with GOE predictions." Hence the NDE routinely is cited as providing striking confirmation of RMT.…”

Section: Testing Rmt With the Ndementioning

confidence: 99%

“…Instead, standard procedure has been to use the theory to correct new data for experimental deficiencies. In the intervening years, random matrix theory (RMT) [2] was developed and has placed the PTD on more formal footing, broadened the scope and predictions, and provided links between nuclear physics and many other fields, including quantum chaos. As a consequence, the impact of neutron resonance data has become much broader, as such data are routinely cited as some of the best proof of the veracity of RMT.…”

Section: Introductionmentioning

confidence: 99%

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Neutron resonance data exclude random matrix theory

Koehler

Bečvář

Krtička

et al. 2012

Fortschritte der Physik

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Key words Porter-Thomas distribution, random matrix theory.Almost since the time it was formulated, the overwhelming consensus has been that random matrix theory (RMT) is in excellent agreement with neutron resonance data. However, over the past few years, we have obtained new neutron-width data at Oak Ridge and Los Alamos National Laboratories that are in stark disagreement with this theory. We also have reanalyzed neutron widths in the most famous data set, the nuclear data ensemble (NDE), and found that it is seriously flawed, and, when analyzed carefully, excludes RMT with high confidence. More recently, we carefully examined energy spacings for these same resonances in the NDE using the ∆3 statistic. We conclude that the data can be found to either confirm or refute the theory depending on which nuclides and whether known or suspected p-wave resonances are included in the analysis, in essence confirming results of our neutron-width analysis of the NDE. We also have examined radiation widths resulting from our Oak Ridge and Los Alamos measurements, and find that in some cases they do not agree with RMT. Although these disagreements presently are not understood, they could have broad impact on basic and applied nuclear physics, from nuclear astrophysics to nuclear criticality safety.

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Section: Testing Rmt With the Ndementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Neutron resonance data exclude random matrix theory

Koehler

Bečvář

Krtička

et al. 2012

Fortschritte der Physik

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“…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].…”

mentioning

confidence: 99%

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

et al. 2016

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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

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“…[5,6,7] reported strong disagreement of neutron resonance data with GOE predictions. Some of these results have found wide attention [8,9,10,11] eroding, as they seemingly do, one of the cornerstones of the statistical theory of nuclear reactions [3,4]. After defining the GOE in Section 2 we address questions (i) and (ii) in turn.…”

Section: Purposementioning

confidence: 99%

“…In its stead one follows Wigner's [1,2] original proposal and uses random-matrix theory (RMT). RMT in its time-reversal invariant form (the Gaussian Orthogonal Ensemble (GOE)) has become a standard tool of nuclear reaction theory [3,4].…”

Section: Purposementioning

confidence: 99%