Related papers: On Landau's eigenvalue theorem and information cut…
This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the…
In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite…
Resonances which result from perturbation of embedded eigenvalues are studied by time dependent methods. A general theory is developed, with new and weaker conditions, allowing for perturbations of threshold eigenvalues and relaxed Fermi…
The concept of bounded variation has been generalized in many ways. In the frame of functions taking values in Banach space, the concept of bounded semivariation is a very important generalization. The aim of this paper is to provide an…
The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…
We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state…
We obtain the phase diagrams of field theories of intertwined orders in the presence of periodic driving by an external field which preserves all symmetries. We consider both a conventional Landau theory of competing orders, and a…
Timelimited functions and bandlimited functions play a fundamental role in signal and image processing. But by the uncertainty principles, a signal cannot be simultaneously time and bandlimited. A natural assumption is thus that a signal is…
In this work, we use regularized determinant approach to study the discrete spectrum generated by relatively compact non-self-adjoint perturbations of the magnetic Schr\"odinger operator $(-i\nabla - \textbf{\textup{A}})^{2} - b$ in…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
We consider linear time-varying channels with additive white Gaussian noise. For a large class of such channels we derive rigorous estimates of the eigenvalues of the correlation matrix of the effective channel in terms of the sampled…
We discuss the requirement of single valuedness and periodicity of eigenfunction of the third component of the operator of angular momentum. This condition, imposed on a non observable, is often used to derive that the eigenvalues of…
We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation…
The purpose of this paper is to extend some spectral properties of regular Sturm-Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with…
This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space…
In the present paper, we deal with a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. A self-adjoint linear operator A is defined in a suitable…
We provide a functional framework and a numerical algorithm to compute the Bloch variety for Maxwell's equations when the electric permittivity is frequency dependent. We incorporate the idea of a mixed formulation for Maxwell's equations…
The transmission eigenvalue problem arises from the inverse scattering theory for inhomogeneous media and has important applications in many qualitative methods. The problem is posted as a system of two second order partial differential…
Rigorous bounds on the rate of energy exchanges between vibrational and translational degrees of freedom are established in simple classical models of diatomic molecules. The results are in agreement with an elementary approximation…
We model the transmission of a message on the complete graph with n vertices and limited resources. The vertices of the graph represent servers that may broadcast the message at random. Each server has a random emission capital that…