Related papers: On Landau's eigenvalue theorem and information cut…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
We consider transfer operators acting on spaces of holomorphic functions, and provide explicit bounds for their eigenvalues. More precisely, if D is any open set in C^d, and L is a suitable transfer operator acting on Bergman space A^2(D),…
This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency…
Time and band limiting operators are expressed as functions of the confluent Heun operator arising in the spheroidal wave equation. Explicit formulas are obtained when the bandwidth parameter is either small or large and results on the…
The macroscopic properties of a quantum system strongly depend on the spreading of the physical eigenfunctions (wavefunctions) of its Hamiltonian operador over its confined domain. The wavefunctions are often controlled by classical or…
This work investigates the effects of time-varying media, where optical properties change over time, on electromagnetic wave propagation, focusing on plane waves and free-electron evanescent waves. We introduce a switching parameter,…
In this letter new, closed and compact analytic expressions for the evaluation of resonant energies, resonant bound-states, eigenvalues and eigenfunctions for both scattering and bounded $n$-cell systems are reported. It is shown that for…
We prove inclusion theorems for both spectra and essential spectra as well as two-sided bounds for isolated eigenvalues for Klein-Gordon type Hamiltonian operators. We first study operators of the form $JG$, where $J$, $G$ are selfadjoint…
Entanglement engineering plays a central role in quantum-enhanced technologies, with potential physical platforms that outperform their classical counterparts. However, free electrons remain largely unexplored despite their great capacity…
We propose a new notion of variable bandwidth that is based on the spectral subspaces of an elliptic operator $A_pf = - (pf')'$ where $p>0$ is a strictly positive function. Denote by $c_{\Lambda} (A_p)$ the orthogonal projection of $A_p$…
The confluence of quantum mechanics and complexity, which leads to the emergence of rich, exotic states of matter, motivates the extension of our concepts of quantum ordering. The twin concepts of spontaneously broken symmetry, described in…
A four-dimensional photon polarization space, such that gives a different interpretation of the ladder operators for the time-like degree comparing to the Gupta-Bleuler formulation is presented. This interpretation, coming from the…
Prolate spheroidal wave functions are an orthogonal family of bandlimited functions on $\mathbb{R}$ that have the highest concentration within a specific time interval. They are also identified as the eigenfunctions of a time-frequency…
The study of degrees of freedom of signals observed within spatially diverse broadband multipath fields is an area of ongoing investigation and has a wide range of applications, including characterising broadband MIMO and cooperative…
A fundamental problem in any communication system is: given a communication channel between a transmitter and a receiver, how many "independent" signals can be exchanged between them? Arbitrary communication channels that can be described…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
This article investigates the full Boltzmann equation up to second order in the cosmological perturbations. Describing the distribution of polarized radiation by a tensor valued distribution function, we study the gauge dependence of the…
The analysis of the fully three-dimensional and time-varying polarization characteristics of a modulated trivariate, or three-component, oscillation is addressed. The use of the analytic operator enables the instantaneous three-dimensional…
The spectral properties of a singular left-definite Sturm-Liouville operator $JA$ are investigated and described via the properties of the corresponding right-definite selfadjoint counterpart $A$ which is obtained by substituting the…
Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type…