相关论文: Eigenvalue correlations on Hyperelliptic Riemann s…

The long-range spectral density correlations (spectral rigidities $\bar{\Delta}_3(\bar n)$ and related spectral compressibilities) of the $E\otimes (b_1+b_2)$ Jahn-Teller model are found strongly nonuniversal with respect to the Hamiltonian…

The integrable structure of Ginibre's Orthogonal Ensemble of random matrices is looked at through the prism of the probability "p_{n,k}" to find exactly "k" real eigenvalues in the spectrum of an "n" by "n" real asymmetric Gaussian random…

In this second part of our series of papers, we develop an abstract framework suitable for de Rham complexes that depend on a parameter belonging to an arbitrary Banach space. Our primary focus is on spectral perturbation problems and the…

We calculate the local correlation functions of charge and spin for the one-chain and two-chain Hubbard model using the density matrix renormalization group method and the recursion technique. Keeping only finite number of states we get…

We study the high-frequency behavior of the Dirichlet-to-Neumann map for an arbitrary compact Riemannian manifold with a non-empty smooth boundary. We show that far from the real axis it can be approximated by a simpler operator. We use…

We establish a spectral representation for solutions to linear Hamilton equations with positive definite energy in a Hilbert space. Our approach is a special version of M. Krein's spectral theory of J-selfadjoint operators is the Hilbert…

The distribution of eigenvalues of N times N random matrices in the limit N to infinity is the solution to a variational principle that determines the ground state energy of a confined fluid of classical unit charges. This fact is a…

Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…

Unitary ensembles of large N x N random matrices with a non-Gaussian probability distribution P[H] ~ exp{-TrV[H]} are studied using a theory of polynomials orthogonal with respect to exponential weights. Asymptotically exact expressions for…

For a broad class of unitary ensembles of random matrices we demonstrate the universal nature of the Janossy densities of eigenvalues near the spectral edge, providing a different formulation of the probability distributions of the limiting…

The eigenvalue statistics for complex $N \times N$ Wishart matrices $X_{r,s}^\dagger X_{r,s}$, where $ X_{r,s}$ is equal to the product of $r$ complex Gaussian matrices, and the inverse of $s$ complex Gaussian matrices, are considered. In…

We try to present an estimate relating the first Dirichlet and Neumann eigenvalues of a compact bordered Riemannian surface.

Let $(G,\kappa)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain…

A density functional theory (DFT) of lattice fermion models is presented, which uses the single-particle density matrix gamma_{ij} as basic variable. A simple, explicit approximation to the interaction-energy functional W[gamma] of the…

We consider a discrete, non-Hermitian random matrix model, which can be expressed as a shift of a rank-one perturbation of an anti-symmetric matrix. We show that, asymptotically almost surely, the real parts of the eigenvalues of the…

It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…

Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices $A_{n}$ and $B_{n}$ rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix $U_{n}$ (i.e.…

We study the spectrum of large a bi-diagonal Toeplitz matrix subject to a Gaussian random perturbation with a small coupling constant. We obtain a precise asymptotic description of the average density of eigenvalues in the interior of the…

In this paper, we compute universal estimates of eigenvalues of a coupled system of elliptic differential equations in divergence form on a bounded domain in Euclidean space. As an application, we show an interesting case of rigidity…

In this paper, we obtain eigenvalue estimates for a larger class of elliptic differential operators in divergence form on a bounded domain in a complete Riemannian manifold isometrically immersed in Euclidean space. As an application, we…