32 research outputs found
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' -parametrized entropy. We discuss the
dependence of the spacing distribution on 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 with , and
, but fails to reproduce the double peaking of the
distribution for the 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