Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2001-03-15
Nonlinear Sciences
Chaotic Dynamics
11 pages Latex and 4 postscript figures
Scientific paper
10.1088/0305-4470/35/10/302
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.
Abul--Magd A. Y.
El-Hady Abd A.
Simbel M. H.
No associations
LandOfFree
Influence of symmetry breaking on the fluctuation properties of spectra does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Influence of symmetry breaking on the fluctuation properties of spectra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Influence of symmetry breaking on the fluctuation properties of spectra will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-565219