The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation of the spectrum of a Schrödinger operator with a disordered potential. Unlike plane waves or Bloch waves that arise as Schrödinger eigenfunctions for period...

The Rosenzweig-Porter random matrix ensemble serves as a qualitative phenomenological model for the level statistics and fractality of eigenstates across many-body localization transition in static systems. We propose unitary (circular) analogue this ensemble, which similarly captures phenomenology periodically driven (Floquet) define outcome Dyson Brownian motion process. show numerical eviden...

Recently developed numerical methods make possible the highaccuracy computation of eigenmodes of the Laplacian for a variety of “drums” in two dimensions. A number of computed examples are presented together with a discussion of their implications concerning bound and continuum states, isospectrality, symmetry and degeneracy, eigenvalue avoidance, resonance, localization, eigenvalue optimizatio...

We consider the Geršgorin disc separation from the origin for (doubly) diagonally dominant matrices and their Schur complements, showing that the separation of the Schur complement of a (doubly) diagonally dominant matrix is greater than that of the original grand matrix. As application we discuss the localization of eigenvalues and present some upper and lower bounds for the determinant of dia...

We analyze the eigenvalues and eigenvectors of the staggered Dirac operator in quenched lattice QCD in the vicinity of the deconfinement phase transition using the Lüscher-Weisz gauge action. The spectral and localization properties of the low-lying eigenmodes show characteristic differences between the Z3 sectors above the critical temperature Tc. These findings can be interpreted in terms of ...

We establish exponential localization for a multi-particle Anderson model in a Euclidean space R, d ≥ 1, in presence of a non-trivial short-range interaction and an alloy-type random external potential. Specifically, we prove that all eigenfunctions with eigenvalues near the lower edge of the spectrum decay exponentially.

Wireless sensor networks attracting a great deal of research interest. Accurate localization of sensor nodes is a strong requirement in a wide area of applications. In recent years, several techniques have been proposed for localization in wireless sensor networks. In this paper we present a localization scheme with using only one mobile anchor station and received signal strength indicator tec...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...