Related papers: Statistics of eigenfunctions in open chaotic syste…
We describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding non-orthogonal eigenvectors for non-Hermitian random matrices modeling one-channel quantum-chaotic scattering in systems…
We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the non-orthogonality of resonance…
Recently, it has been shown that the change of resonance widths in an open system under a perturbation of its interior is a sensitive indicator of the nonorthogonality of resonance states. We apply this measure to quantify parametric motion…
The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a…
We present experimental results on the eigenfrequency statistics of a superconducting, chaotic microwave billiard containing a rotatable obstacle. Deviations of the spectral fluctuations from predictions based on Gaussian orthogonal…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
In this letter, we demonstrate that a non-Hermitian Random Matrix description can account for both spectral and spatial statistics of resonance states in a weakly open chaotic wave system with continuously distributed losses. More…
. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of…
We numerically analyze the statistical properties of complex system with conditions subjecting the matrix elements to a set of specific constraints besides symmetry, resulting in various structures in their matrix representation. Our…
It is generally accepted that statistics of energy levels in closed chaotic quantum systems is adequately described by the theory of Random Hermitian Matrices. Much less is known about properties of "resonances" - generic features of open…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
Non-hermitian systems have gained a lot of interest in recent years. However, notions of chaos and localization in such systems have not reached the same level of maturity as in the Hermitian systems. Here, we consider non-hermitian…
We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of…
We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical…
The spectral statistics of non-Hermitian random matrices are of importance as a diagnostic tool for chaotic behavior in open quantum systems. Here, we investigate the statistical properties of singular values in non-Hermitian random…
In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
The statistics of chiral matrix ensembles with uncorrelated but multivariate Gaussian distributed elements is intuitively expected to be driven by many parameters. Contrary to intuition, however, our theoretical analysis reveals the…
A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of…