Related papers: Spectral Measures on Locally Fields
We construct the analogue of the Serre spectral sequence for the bounded cohomology of simplicial sets with seminormed local coefficients. As applications, we obtain a (non-isometric) generalization of Gromov's mapping theorem and some…
A random matrix theory approach is applied in order to analyze the localization properties of local spectral density for a generic system of coupled quantum states with strong static imperfection in the unperturbed energy levels. The system…
A measure on a locally compact Abelian group is said to have a natural spectrum if its spectrum is equal to the closure of the range of the Fourier-Stieltjes transform. In this paper we continue the study of spectrally reasonable measures…
We present a rigorous spectral analysis of plasmonic resonances in the nonlocal regime of spatially dispersive media. We adopt the quasi-static approximation of the hydrodynamic Drude model, which provides an analytically tractable setting…
Let $Q$ be a fundamental domain of some full-rank lattice in ${\Bbb R}^d$ and let $\mu$ and $\nu$ be two positive Borel measures on ${\Bbb R}^d$ such that the convolution $\mu\ast\nu$ is a multiple of $\chi_Q$. We consider the problem as to…
The problem of the measurability of the electromagnetic field is investigated 1) in the framework of the abstract restricted-path-integral method, and 2) by explicitly accounting the action of the field onto the meter and its back reaction.…
Lately, much interest has been directed towards designing setups that achieve decisive tests of local realism. Here we present Bell tests with measurements based on linear optical displacements and single-photon detection. The scheme…
We investigate the spectral degree of freedom of OAM-carrying localized waves, and its influence on their transverse intensity distribution. In particular, we focus our attention on two different families of spectra, namely exponentially…
We have numerically implemented a perturbation series for the scattered electromagnetic fields above rough surfaces, due to Greffet, allowing us to evaluate the local density of states to second order in the surface profile function. We…
Given a surface $M$ and a Borel probability measure $\nu$ on the group of $C^2$-diffeomorphisms of $M$, we study $\nu$-stationary probability measures on $M$. We prove for hyperbolic stationary measures the following trichotomy: either the…
We study the dimension properties of the spectral measure of the Circular $\beta$-Ensembles. For $\beta \geq 2$ it it was previously shown by Simon that the spectral measure is almost surely singular continuous with respect to Lebesgue…
We calculate the local density of states of a two-dimensional electron system under strong crossed magnetic and electric fields. We assume a strong perpendicular magnetic field which, in the absence of in-plane electric fields and collision…
We suggest a novel approach for probing of local fluctuations of the refractive index $n$ in solids by means of single-molecule (SM) spectroscopy. It is based on the dependence $T_1(n)$ of the effective radiative lifetime $T_1$ of dye…
We propose a new approach to the spectral theory of perturbed linear operators , in the case of a simple isolated eigenvalue. We obtain two kind of results: ''radius bounds'' which ensure perturbation theory applies for perturbations up to…
We consider small perturbations of expanding maps induced by skew-product mappings whose base dynamics are not invertible necessarily. Adopting a previously developed perturbative spectral approach, we show stability of the densities of the…
Linear (spectro) polarimetry is usually performed using separate photon flux measurements after spatial or temporal polarization modulation. Such classical polarimeters are limited in sensitivity and accuracy by systematic effects and…
Scattering of a short (much shorter then the spontaneous lifetime) laser pulse has been considered in a dense resonant medium subject to local field effects. The system was studied in the limit of Hartree-Fock approximation for…
We obtain a refinement of the degrees of freedom estimate of Landau and Pollak. More precisely, we estimate, in terms of $\epsilon$, the increase in the degrees of freedom resulting upon allowing the functions to contain a certain…
The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…
We investigate the geometric implications of spectral curvature bounds, extending classical rigidity results in scalar curvature geometry to the spectral setting. By systematically employing the warped $\mu$-bubble method, we show…