Publications (5)0 Total impact
-
[show abstract]
[hide abstract]
ABSTRACT: We study the symmetry breaking of acoustic resonances measured by Ellegaard
et al., Phys. Rev. Lett. 77, 4918 (1996), in quartz blocks. The observed
resonance spectra show a gradual transition from a superposition of two
uncoupled components, one for each symmetry realization, to a single component
well represented by a Gaussian orthogonal ensemble (GOE) of random matrices. We
discuss the applicability of superstatistical random-matrix theory to the final
stages of the symmetry breaking transition. A comparison is made between
different formula of the superstatistics and a pervious work [Abd El-Hady et
al, J. Phys. A: Math. Theor. 35, 2361 (2002)], which describes the same data by
introducing a third GOE component. Our results suggest that the
inverse-chi-square superstatistics could be used for studying the whole
symmetry breaking process.
01/2012;
-
[show abstract]
[hide abstract]
ABSTRACT: We present a possible extension of the random-matrix theory, which is widely
used to describe spectral fluctuations of chaotic systems. By considering the
Kaniadakis non-Gaussian statistics, characterized by the index {\kappa}
(Boltzmann-Gibbs entropy is recovered in the limit {\kappa}\rightarrow0), we
propose the non-Gaussian deformations ({\kappa} \neq 0) of the conventional
orthogonal and unitary ensembles of random matrices. The joint eigenvalue
distributions for the {\kappa}-deformed ensembles are derived by applying the
principle maximum entropy to Kaniadakis entropy. The resulting distribution
functions are base invarient as they depend on the matrix elements in a trace
form. Using these expressions, we introduce a new generalized form of the
Wigner surmise valid for nearly-chaotic mixed systems, where a
basis-independent description is still expected to hold. We motivate the
necessity of such generalization by the need to describe the transition of the
spacing distribution from chaos to order, at least in the initial stage. We
show several examples about the use of the generalized Wigner surmise to the
analysis of the results of a number of previous experiments and numerical
experiments. Our results suggest the entropic index {\kappa} as a measure for
deviation from the state of chaos. We also introduce a {\kappa}-deformed
Porter-Thomas distribution of transition intensities, which fits the
experimental data for mixed systems better than the commonly-used
gamma-distribution.
01/2012;
-
[show abstract]
[hide abstract]
ABSTRACT: We consider the possibility of identifying nuclei exhibiting the SU(3) dynamical symmetry as those having excitation energy ratio R4/2 >= 3.25. For this purpose, we consider the level statistics of some of these nuclei and perform interacting boson model (IBM) calculation of level schemes, and electromagnetic transition rates. We show that only some of these nuclei may be considered as good examples of the SU(3) dynamical symmetry. Comment: 10 pages, 2 figures, to be published in Nuclear Physics A
03/2010;
-
A. Y. Abul-Magd
[show abstract]
[hide abstract]
ABSTRACT: Random matrix theory (RMT) is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Most of the proposed generalizations keep the first assumption and violate the second. Recently, several authors presented other versions of the theory that keep base invariance on the expense of allowing correlations between matrix elements. This is achieved by starting from non-extensive entropies rather than the standard Shannon entropy, or following the basic prescription of the recently suggested concept of superstatistics. We review these generalizations of RMT and illustrate their value by calculating the nearest-neighbor-spacing distributions and comparing the results of calculation with experiments and numerical-experiments on systems in transition from order to chaos. Comment: 25 pages, 2 figures
02/2009;
-
[show abstract]
[hide abstract]
ABSTRACT: The nearest neighbor spacing distribution of levels of deformed even-even nuclei classified according to their quadrupole deformation parameter is investigated. The results suggest that the oblate deformed nuclei have more regular spectra than prolate ones.
06/2006;
