相关论文: Green's Functions in Non-hermitian Random Matrix M…

This paper is a detailed account of the recent progress in understanding the statistical properties of complex eigenvalues of random non-Hermitian matrices reported earlier in our two short communications: Physics Letters A v.226, 46 (1997)…

We introduce a powerful analytic method to study the statistics of the number $\mathcal{N}_{\textbf{A}}(\gamma)$ of eigenvalues inside any contour $\gamma \in \mathbb{C}$ for infinitely large non-Hermitian random matrices ${\textbf A}$. Our…

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…

We compare the Ornstein-Uhlenbeck process for the Gaussian Unitary Ensemble to its non-hermitian counterpart - for the complex Ginibre ensemble. We exploit the mathematical framework based on the generalized Green's functions, which…

In this paper, we employ the generalized Bloch theory to rediscover the generalized Brillouin zone theory and follow this way to obtain the Green's function of the non-Hermitian system. We focus on a classical chiral model and give the…

We generalize the methods used in the theory of correlation dynamics and establish a set of equations of motion for many-body correlation green's functions in the non-relativistic case. These non-linear and coupled equations of motion…

The well-known Green's function method has been recently generalized to nonlinear second order differential equations. In this paper we study possibilities of exact Green's function solutions of nonlinear differential equations of higher…

Non-Hermitian systems have garnered significant attention due to the emergence of novel topology of complex spectra and skin modes. However, investigating transport phenomena in such systems faces obstacles stemming from the non-unitary…

In this paper, we establish a connection between the formalism of $\mathcal{R}$-transforms for non-Hermitian random matrices and the framework of spherical integrals, using the replica method. This connection was previously proved in the…

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…

Green's functions are fundamental quantities that determine the linear responses of physical systems. The recent developments of non-Hermitian systems, therefore, call for Green's function formulas of non-Hermitian bands. This task is…

Statistical properties of eigenvectors in non-Hermitian random matrix ensembles are discussed, with an emphasis on correlations between left and right eigenvectors. Two approaches are described. One is an exact calculation for Ginibre's…

We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…

Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…

We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble…

We study the Brown measure of certain non-hermitian operators arising from Voiculescu's free probability theory. Usually those operators appear as the limit in *-moments of certain ensembles of non-hermitian random matrices, and the Brown…

A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex…

A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…