Neutron resonance spectroscopy: Ta

Hacken, G.; Werbin, R.; Rainwater, J.

doi:10.1103/physrevc.17.43

Cited by 24 publications

(8 citation statements)

References 3 publications

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“…This indicates the presence of two independent symmetry sectors, and is indeed the case, as confirmed in Refs. [14,45]. This measured sequence consists of a superposition of levels having angular momenta J = 3 and 4, and when symmetry decomposed, are in broad agreement with the Wigner surmise.…”

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confidence: 67%

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Symmetry deduction from spectral fluctuations in complex quantum systems

Tekur

Santhanam

2020

Phys. Rev. Research

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The spectral fluctuations of complex quantum systems, in an appropriate limit, are known to be consistent with those obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices is valid only if the spectra are desymmetrized. This implies that the fluctuation properties of the spectra are affected by the discrete symmetries of the system. In this Rapid Communication, it is shown that in the chaotic limit the fluctuation characteristics and symmetry structure for any arbitrary sequence of measured or computed levels can be inferred from its higher-order spectral statistics without desymmetrization. In particular, we consider a spectrum composed of k > 0 independent level sequences with each sequence having the same level density. The kth order spacing ratio distribution of such a composite spectrum is identical to its nearest-neighbor counterpart with a modified Dyson index k. This is demonstrated for the spectra obtained from random matrices, quantum billiards, spin chains, and experimentally measured nuclear resonances with disparate symmetry features.

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supporting

confidence: 67%

“…It is assumed that the system being observed is in the putative regime in which RMT results can be applied. We consider a sequence of experimentally observed neutron resonances for a Ta 181 nucleus [45] whose NN spacing distribution, discussed in Ref. [14], does not match the Wigner surmise.…”

mentioning

confidence: 99%

Symmetry deduction from spectral fluctuations in complex quantum systems

Tekur

Santhanam

2020

Phys. Rev. Research

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“…Regardless of the underlying interactions, e. g., nuclear or electromagnetic, if certain symmetries are obeyed, the eigenvalues of these matrices should mimic the behavior of the energy spectrum of these complicated states. This has been verified experimentally for many nuclei [2] and also for some atoms [3]. There are three different ensembles of matrices associated with randommatrix theory (RMT}: the Gaussian orthogonal (GOE}, unitary (GUE} and symplectic ensembles.…”

Section: Introductionmentioning

confidence: 78%

Statistical behavior of eigenvalues of real-symmetric and complex-Hermitian band matrices: Comparison with random-matrix theory

Hs¹

1992

Phys. Rev. A

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Numerical calculations have been performed with real-symmetric and complex-Hermitian matrices of dimension N having nonzero random matrix elements within a relatively narrow band of width M. It is shown that if the ratio M/N is held fixed as the matrix dimension N increases, a sequence of n eigenvalues will exhibit statistical behavior in good agreement with the predicted statistical behavior of the eigenvalues associated with the Gaussian orthogonal and the Gaussian unitary ensembles of randommatrix theory.PACS number(sj: 05.40. +j, 24.60.Ky, 05.45.+b

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“…It has been observed experimentally [1,2] for disordered systems that the distribution of the energy levels of such systems is universal in some regime. For instance the connected correlation function between two levels separated by a small number of other levels does not depend on the system, while the density of levels is very dependent of the specific details of the system.…”

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confidence: 99%

Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices

Eynard

1997

Nuclear Physics B

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Abstract:It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of this distribution in two classes of random hermitian matrix models: the one-matrix model, and the two-matrix model, although it seems that the methods and conclusions presented here will allow generalization to other multi-matrix models such as the chain of matrices, or the O(n) model. We recover the universality of the two point function in two regimes: short distance regime when the two eigenvalues are separated by a small number of other eigenvalues, and on the other hand the long range regime, when the two eigenvalues are far away in the spectrum, in this regime we have to smooth the short scale oscillations. We also discuss the universality properties of more than two eigenvalues correlation functions.

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Neutron resonance spectroscopy: Ta

Cited by 24 publications

References 3 publications

Symmetry deduction from spectral fluctuations in complex quantum systems

Symmetry deduction from spectral fluctuations in complex quantum systems

Statistical behavior of eigenvalues of real-symmetric and complex-Hermitian band matrices: Comparison with random-matrix theory

Eigenvalue distribution of large random matrices, from one matrix to several coupled matrices

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