598 research outputs found
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.Comment: accepted for publication in Physical Review
Effect of Unfolding on the Spectral Statistics of Adjacency Matrices of Complex Networks
Random matrix theory is finding an increasing number of applications in the
context of information theory and communication systems, especially in studying
the properties of complex networks. Such properties include short-term and
long-term correlation. We study the spectral fluctuations of the adjacency of
networks using random-matrix theory. We consider the influence of the spectral
unfolding, which is a necessary procedure to remove the secular properties of
the spectrum, on different spectral statistics. We find that, while the spacing
distribution of the eigenvalues shows little sensitivity to the unfolding
method used, the spectral rigidity has greater sensitivity to unfolding.Comment: Complex Adaptive Systems Conference 201
The effect of nuclear deformation on level statistics
We analyze the nearest neighbor spacing distributions of low-lying 2+ levels
of even-even nuclei. We grouped the nuclei into classes defined by the
quadrupole deformation parameter (Beta2). We calculate the nearest neighbor
spacing distributions for each class. Then, we determine the chaoticity
parameter for each class with the help of the Bayesian inference method. We
compare these distributions to a formula that describes the transition to chaos
by varying a tuning parameter. This parameter appears to depend in a
non-trivial way on the nuclear deformation, and takes small values indicating
regularity in strongly deformed nuclei and especially in those having an oblate
deformation.Comment: 10 Pages, 6 figure
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