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.Comment: 26 pages, 3 figures; v3: changed conclusions, appendix adde

Spectral fluctuation properties of spherical nuclei

The spectral fluctuation properties of spherical nuclei are considered by use of NNSD statistic. With employing a generalized Brody distribution included Poisson, GOE and GUE limits and also MLE technique, the chaoticity parameters are estimated for sequences prepared by all the available empirical data. The ML-based estimated values and also KLD measures propose a non regular dynamic. Also, spherical odd-mass nuclei in the mass region, exhibit a slight deviation to the GUE spectral statistics rather than the GOE.Comment: 10 pages, 2 figure

Analysis of symmetry breaking in quartz blocks using superstatistical random matrix theory

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.Comment: 11 pages, 1 figur

Modelling gap-size distribution of parked cars using random-matrix theory

We apply the random-matrix theory to the car-parking problem. For this purpose, we adopt a Coulomb gas model that associates the coordinates of the gas particles with the eigenvalues of a random matrix. The nature of interaction between the particles is consistent with the tendency of the drivers to park their cars near to each other and in the same time keep a distance sufficient for manoeuvring. We show that the recently measured gap-size distribution of parked cars in a number of roads in central London is well represented by the spacing distribution of a Gaussian unitary ensemble.Comment: 7 pages, 1 figur

Non-extensive Random Matrix Theory - A Bridge Connecting Chaotic and Regular Dynamics

We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' $q$-parametrized entropy. We discuss the dependence of the spacing distribution on $q$ using a non-extensive generalization of Wigner's surmises for ensembles belonging to the orthogonal, unitary and symplectic symmetry universal classes.Comment: Accepted for publication in Physics Letters

Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A \textbf{322}, (2003), 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.Comment: 18 page

Discrete structures in fusion-barrier distributions for vibrational nuclei

We obtain a closed-form expression for the distribution of fusion barriers for vibrational nuclei using a generalization of Dasso, Landowne, and Winther's model, which represents the nuclear surface vibrations as a number of harmonic oscillators, and allows the excitation of an arbitrary number of phonons in the target and/or projectile. We find that this expression is in reasonable agreement with the average trends of the empirical distributions for the fusion of $\mathsf{^{16}O}$ with $\mathsf{^{92}Zr}$, $\mathsf{^{144}Sm}$ and $\mathsf{^{208}Pb}$, but fails to reproduce the double peaking of the distribution for the $\mathsf{^{144}Sm}$ target. Only when we restrict the number of excited phonons to a limited number, we are able to reproduce such discrete structures. We show that limiting the number of coupled channels, particularly in the case of strong coupling, increases the spacings between the channel eigenvalues that determine the positions of the peaks of the barrier distribution and modifies their heights