105 research outputs found
Nonextensive and superstatistical generalizations of random-matrix theory
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 figure
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
Superstatistics in Random Matrix Theory
Random matrix theory (RMT) provides a successful model for quantum systems,
whose classical counterpart has a chaotic dynamics. It is based on two
assumptions: (1) matrix-element independence, and (2) base invariance. Last
decade witnessed several attempts to extend RMT to describe quantum systems
with mixed regular-chaotic dynamics. 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. The latter concept was introduced as a generalization of
equilibrium thermodynamics to describe non-equilibrium systems by allowing the
temperature to fluctuate. We here review the superstatistical generalizations
of RMT and illustrate their value by calculating the nearest-neighbor-spacing
distributions and comparing the results of calculation with experiments on
billiards modeling systems in transition from order to chaos.Comment: Invited Talk, 2nd International Conference on Numerical Analysis and
Optimization, Muscat, Oman, 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
- …