Related papers: The Spectral Shift Function and The Friedel Sum Ru…
The superscaling function extracted from inclusive electron scattering data is used to predict high energy charge-changing neutrino cross sections in the quasi-elastic and $\Delta$ regions.
In this tutorial paper, we consider the problem of electromagnetic scattering by a bounded two-dimensional dielectric object, and discuss certain interesting properties of the scattered field. Using the electric field integral equation,…
We prove new upper bounds for a spectral exponential sum by refining the process by which one evaluates mean values of $L$-functions multiplied by an oscillating function. In particular, we introduce a method which is capable of taking into…
In this note the notions of trace compatible operators and infinitesimal spectral flow are introduced. We define the spectral shift function as the integral of infinitesimal spectral flow. It is proved that the spectral shift function thus…
We present a theory of light scattering consistent with modern physics. We proposed a spatial-temporal model of a photon based on classical model of atomic oscillator. Using this photon model, we established a criterion for single vs…
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…
The statistics of energy levels of electrons in a random potential is considered in the critical energy window near the mobility edge. It is shown that the multifractality of critical wave functions results in the violation of the…
The current status of the Adler function and two closely related Deep Inelastic Scattering (DIS) sum rules, namely, the Bjorken sum rule for polarized DIS and the Gross-Llewellyn Smith sum rule are briefly reviewed. A new result is…
We consider the scattering theory for the defocusing energy subcritical wave equations with an inverse square potential. By employing the energy flux method we establish energy flux estimates on the light cone. Then by the characteristic…
At a Fano resonance in a quantum wire there is strong quantum mechanical back-scattering. When identical wave packets are incident along all possible modes of incidence, each wave packet is strongly scattered. The scattered wave packets…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
4D CFTs have a scale anomaly characterized by the coefficient $c$, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point…
We study scattering theory identities previously obtained as consistency conditions in the context of one-loop quantum field theory calculations. We prove the identities using Jost function techniques and study applications.
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
We introduce a spectral density functional theory which can be used to compute energetics and spectra of real strongly--correlated materials using methods, algorithms and computer programs of the electronic structure theory of solids. The…
We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal…
The neutron and proton single-particle spectral functions in asymmetric nuclear matter fulfill energy weighted sum rules. The validity of these sum rules within the self-consistent Green's function approach is investigated. The various…
We show that the leading double spectral density in sum rules for Compton-like processes can be obtained by simple properties of the Borel transform, extending an approach widely used in the literature on sum rules, and known to be valid…
The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum…
The present article deals with differential equations with spectral parameter from the point of view of formal power series. The treatment does not make use of the notion of eigenvalue, but introduces a new idea: the spectral residue. The…