arXiv subjects

M. H. Simbel

Publications and source records attributed to M. H. Simbel.

6 recordsLinked to original sources

arXiv2005

Cross correlation of low-lying levels of even-even nuclei

We consider the cross correlations of low-lying energy levels of nuclei belonging to small intervals of the excitation-energy ratio R_{4/2} of the first 4^+ to 2^+ states. The mean value of the cross-correlation coefficients, plotted as a function of R_{4/2} has deep minima at values of R_{4/2}=2.2 and 2.9, which correspond to the critical dynamical symmetries of the interacting Boson model. The distribution of the calculated coefficients for nuclei belonging to different R_{4/2} classes has different pattern.

cond-mat.stat-mech↗

arXiv2004

Statistics of 2+ Levels in Even-Even Nuclei

Using all the available empirical information, we analyze the spacing distributions of low-lying 2-plus levels of even-even nuclei. To obtain statistically relevant samples, the nuclei are grouped into classes defined by the ratio R4/2 of the excitation energies of the first 4-plus and 2-plus levels. This ratio serves as a measure of collectivity in nuclei. With the help of Bayesian inference, we determine the chaoticity parameter for each class. This parameter is found to vary strongly with R4/2 and takes particularly small values in nuclei that have one of the dynamical symmetries of the interacting Boson model.

nucl-th↗

arXiv2004

Statistical Analysis of Composite Spectra

We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of such data. One problem lies in fitting the nearest neighbor spacing distribution to the histogram of level spacings obtained from the data. We show that the method of Bayesian inference is superior to this procedure. The second problem occurs when one unfolds such short sequences. We show that the unfolding procedure generically leads to an overestimate of the chaoticity parameter. This trend is absent in the presence of long-range level correlations. Thus, composite ensembles of levels from a system with long-range spectral stiffness yield reliable information about the chaotic behavior of the system.

physics.data-an↗

arXiv2004

Phenomenological model for symmetry breaking in chaotic system

We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the fractional level densities of the sequences and the symmetry breaking interaction is deduced by comparing the asymptotic expression of the level-number variance with the corresponding expression obtained using the perturbation theory. This relation is supported by a comparison with previous numerical calculations. The predictions of the model for the nearest-neighbor-spacing distribution and the spectral rigidity are in agreement with the results of an acoustic resonance experiment.

cond-mat.stat-mech↗

arXiv2003

Regularity and Chaos in low-lying 2+ states of even-even nuclei

Using all the available empirical information, we analyse the spacing distributions of low-lying 2+ levels in even-even nuclei by comparing them with a theoretical distribution characterized by a single parameter (the chaoticity parameter f). We use the method of Bayesian inference. We show that the necessary unfolding procedure generally leads to an overestimate of f. We find that f varies strongly with the ratio of the excitation energies of the first 4+ and 2+ levels and assumes particularly small values in nuclei that have one of the dynamical symmetries of the Interacting Boson Model.

nucl-th↗

arXiv2001

Influence of symmetry breaking on the fluctuation properties of spectra

We study the effect of gradual symmetry breaking in a non-integrable system on the level fluctuation statistics. We consider the case when the symmetry is represented by a quantum number that takes one of two possible values, so that the unperturbed system has a spectrum composed of two independent sequences. When symmetry-breaking perturbation is represented by a random matrix with an adjustable strength, the shape of the spectrum monotonously evolves towards the Wigner distribution as the strength parameter increases. This contradicts the observed behaviour of the acoustic resonance spectra in quartz blocks during the breaking of a point-group symmetry that has two eigenvalues, where the system changes in the beginning towards the Poisson statistics then turns back to the GOE statistics. This behaviour is explained by assuming that the symmetry breaking perturbation removes the degeneracy of a limited number of levels, thus creating a third chaotic sequence. As symmetry breaking increases, the new sequence grows at the expense of the initial pair until it overwhelms the whole spectrum when the symmetry completely disappears. The calculated spacing distribution and spectral rigidity are able to describe the evolution of the observed acoustic resonance spectra.

nlin.CD↗