Pseudo-Hermitian anti-Hermitian ensemble of Gaussian matrices.

It is shown that the ensemble of pseudo-Hermitian Gaussian matrices recently introduced gives rise in a certain limit to an ensemble of anti-Hermitian matrices whose eigenvalues have properties directly related to those of the chiral ensemble of random matrices.

Pseudo-Hermitian ensemble of random Gaussian matrices.

It is shown how pseudo-Hermiticity, a necessary condition satisfied by operators of PT symmetric systems can be introduced in the three Gaussian classes of random matrix theory. The model describes transitions from real eigenvalues to a situation in which, apart from a residual number, the eigenvalues are complex conjugate.

Missing levels in acoustic resonators.

It is shown that the deviations of the experimental statistics of six chaotic acoustic resonators from Wigner-Dyson random matrix theory predictions are explained by a recent model of random missing levels. In these resonatorsa made of aluminum plates a the larger deviations occur in the spectral rigidity (SRs) while the nearest-neighbor distributions (NNDs) are still close to the Wigner surmise. Good fits to the experimental NNDs and SRs are obtained by adjusting only one parameter, which is the fraction of remaining levels of the complete spectra. For two Sinai stadiums, one Sinai stadium without planar symmetry, two triangles, and a sixth of the three-leaf clover shapes, was found that 7%, 4%, 7%, and 2%, respectively, of eigenfrequencies were not detected.

Level density for deformations of the Gaussian orthogonal ensemble.

Formulas are derived for the average level density of deformed, or transition, Gaussian orthogonal random matrix ensembles. After some general considerations about Gaussian ensembles, we derive formulas for the average level density for (i) the transition from the Gaussian orthogonal ensemble (GOE) to the Poisson ensemble and (ii) the transition from the GOE to m GOEs.

Universality of rescaled curvature distributions.

We applied a recently proposed rescaling of curvatures of eigenvalues of parameter-dependent random matrices to experimental data from acoustic systems and to a theoretical result. It is found that the data from four different experiments, ranging from isotropic plates to anisotropic three-dimensional objects, and the theoretical result always agree with the universal curvature distribution, if only the curvatures are rescaled such that the average of their absolute values is unity.

Family of generalized random matrix ensembles.

Using the generalized maximum entropy principle based on the nonextensive q entropy, a family of random matrix ensembles is generated. This family unifies previous extensions of random matrix theory (RMT) and gives rise to an orthogonal invariant stable Lévy ensemble with new statistical properties. Some of them are analytically derived.

Effect of symmetry breaking on level curvature distributions.

We derive an exact general formalism that expresses the eigenvector and the eigenvalue dynamics as a set of coupled equations of motion in terms of the matrix elements dynamics. Combined with an appropriate model Hamiltonian, these equations are used to investigate the effect of the presence of a discrete symmetry in the level curvature distribution. An explanation of the unexpected behavior of the data regarding frequencies of acoustic vibrations of quartz block is provided.