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

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

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