Broken Symmetries and Chaotic Behavior in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>26</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>

Mitchell, G. E.; Bilpuch, E.G.; Endt, P.M.; Shriner, J. F.

doi:10.1103/physrevlett.61.1473

Cited by 118 publications

(78 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Experimentally the distribution is intermediate between the one-GOE and two-GOE distributions [7,8,10]. This agrees with predictions, fi rst by Dyson [18] and later by Pandey [19] There are no other direct tests in nuclei, but there are extensive results in " analog" systems: acoustic resonances in quartz blocks [21] and electromagnetic resonances in in superconducting microwave billiards [22].…”

Section: Effect Of Isospin Symmetry Breaking On Level Statisticssupporting

confidence: 75%

See 1 more Smart Citation

Statistical behavior and symmetry tests

Mitchell¹,

Shriner²

2004

Braz. J. Phys.

Self Cite

View full text Add to dashboard Cite

Symmetries and statistical properties in nuclei are closely related. The most striking example is the extremely large enhancement of parity violation in neutron resonances. Statistical distributions can provide information about the underlying character of nuclear properties. Level statistics and electromagnetic transition distributions have been used successfully to provide unique tests of predictions of random matrix theory.

show abstract

Section: Effect Of Isospin Symmetry Breaking On Level Statisticssupporting

confidence: 75%

“…We have performed a series of measurements on the effect of isospin symmetry breaking on level statistics [7,8] and on electromagnetic transitions [9,10]. The most striking feature is that a small symmetry breaking can have a large impact on the level statistics and on the transition distributions.…”

Section: Introductionmentioning

confidence: 99%

Statistical behavior and symmetry tests

Mitchell¹,

Shriner²

2004

Braz. J. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Furthermore, the analysis of the spectral properties of experimentally determined bound states of nuclei did not yield the results expected in nuclear many-body systems exhibiting a chaotic dynamics. For light nuclei this was attributed to the insufficient number of identified bound states, and for nuclei like 26 Al and 30 P to the partial isospin symmetry breaking [38,39]. The present analysis of the experimental data is based on the 151 bound states with unambiguously assigned parity and spin [1], so the results are statistically significant.…”

mentioning

confidence: 83%

Chaos and Regularity in the Doubly Magic NucleusPb208

et al. 2017

View full text Add to dashboard Cite

High resolution experiments have recently lead to a complete identification (energy, spin, and parity) of 151 nuclear levels up to an excitation energy of Ex = 6.20 MeV in 208 Pb [Heusler et al., Phys. Rev. C 93, 054321 (2016)]. We present a thorough study of the fluctuation properties in the energy spectra of the unprecedented set of nuclear bound states. In a first approach we grouped states with the same spin and parity into 14 subspectra, analyzed standard statistical measures for short-and long-range correlations, i.e., the nearest-neighbor spacing distribution, the number variance Σ 2 , the Dyson-Mehta ∆3 statistics, and the novel distribution of the ratios of consecutive spacings of adjacent energy levels in each energy sequence and then computed their ensemble average. Their comparison with a random matrix ensemble which interpolates between Poisson statistics expected for regular systems and the Gaussian Orthogonal Ensemble (GOE) predicted for chaotic systems shows that the data are well described by the GOE. In a second approach, following an idea of Rosenzweig and Porter [Phys. Rev. 120, 1698Rev. 120, (1960] we considered the complete spectrum composed of the independent subspectra. We analyzed their fluctuation properties using the method of Bayesian inference involving a quantitative measure, called the chaoticity parameter f , which also interpolates between Poisson (f = 0) and GOE statistics (f = 1). It turns out to be f ≈ 0.9. This is so far the closest agreement with GOE observed in spectra of bound states in a nucleus. The same analysis has also been performed with spectra computed on the basis of shell model calculations with different interactions (SDI, KB, M3Y). While the simple SDI exhibits features typical for nuclear many-body systems with regular dynamics, the other, more realistic interactions yield chaoticity parameters f close to the experimental values.

show abstract

“…Good examples of the experimental and theoretical efforts already invested into this problem, are the cases of isospin mixing [16][17][18], of parity violation in heavy nuclei [19], of the breaking of certain atomic and molecular symmetries [15,20]. The experiment performed in [1] provides a general model for these case studies.…”

Section: Figmentioning

confidence: 99%

Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference

Barbosa

Harney

2000

Phys. Rev. E

View full text Add to dashboard Cite

Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes of levels. The number variance is used to quantify the level fluctuations as a function of the coupling and to construct the conditional probability distribution of the data. The prior distribution of the coupling parameter is obtained from an invariance argument on the entropy of the posterior distribution.

show abstract

Broken Symmetries and Chaotic Behavior inAl26

Cited by 118 publications

References 25 publications

Statistical behavior and symmetry tests

Statistical behavior and symmetry tests

Chaos and Regularity in the Doubly Magic NucleusPb208

Analyzing symmetry breaking within a chaotic quantum system via Bayesian inference

Contact Info

Product

Resources

About