相关论文: Spectral statistics of multi-parametric Gaussian e…

Multi-parametric chiral random matrix ensembles are important tools to analyze the statistical behavior of generic complex systems with chiral symmetry. A recent study \cite{psmulti} of the former maps them to the chiral Brownian ensemble…

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 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…

A statistical description of part of a many body system often requires a non-Hermitian random matrix ensemble with nature and strength of randomness sensitive to underlying system conditions. For the ensemble to be a good description of the…

Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a…

. 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 analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…

We describe Generalized Hermitian matrices ensemble sometimes called Chiral ensemble. We give global asymptotic of the density of eigenvalues or the statistical density. We will calculate a Laplace transform of such a density for finite…

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply…

We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on a non-interacting Fermi-gas we show that for energy differences less than a critical…

We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…

We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U (1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a…

The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the…

We numerically analyze the random matrix ensembles of real-symmetric matrices with column/row constraints for many system conditions e.g. disorder type, matrix-size and basis-connectivity. The results reveal a rich behavior hidden beneath…

Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are…

The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…

We find the microscopic spectral densities and the spectral correlators associated with multicritical behavior for both hermitian and complex matrix ensembles, and show their universality. We conjecture that microscopic spectral densities…

Topological invariance is a powerful concept in different branches of physics as they are particularly robust under perturbations. We generalize the ideas of computing the statistics of winding numbers for a specific parametric model of the…

General statistical ensembles in the Hamiltonian formulation of hybrid quantum-classical systems are analyzed. It is argued that arbitrary probability densities on the hybrid phase space must be considered as the class of possible…

We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic…