Related papers: Operator expansion for high-energy scattering
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities.…
The acoustic scattering operator on the real line is mapped to a Schr\"odinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse…
I discuss recent progress in understanding the high-energy evolution in QCD, which points towards a remarkable correspondence with the reaction-diffusion problem of statistical physics. This enables us to determine the asymptotic behaviour…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
The various motivations for improving the perturbative prediction to next-to-next-to-leading order (NNLO) for basic scattering processes in proton-(anti)proton, electron-proton and electron-positron scattering are discussed in detail.…
We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma}. For 0 < gamma < or =1 we prove the…
This paper presents an investigation of organic LED extraction efficiency enhancement using a low refractive index scattering layer. A scattering model is developed based on rigorous electromagnetic modelling techniques. The model accounts…
We review recent progress on the calculation of scattering amplitudes in the high-energy limit. We start by illustrating the shockwave formalism, which allows one to calculate amplitudes as iterated solutions of rapidity evolution…
We discuss the QCD evolution equations governing the high energy behavior of scattering amplitudes at the leading logarithmic level. This hierarchy of equations accommodates normal BFKL dynamics, Pomeron mergings and Pomeron splittings.…
We prove large-data scattering and existence of wave operators in the energy space for the systems of $N$ defocusing fourth-order Schr\"odinger equations with mass-supercritical and energy-subcritical power-type nonlinearity. In addition,…
Developments of nonlocal operators for modeling processes that traditionally have been described by local differential operators have been increasingly active during the last few years. One example is peridynamics for brittle materials and…
We obtain a simple analytic expression for the high energy $\gamma^* \gamma^*$ scattering cross section at the next-to-leading order in the logarithms-of-energy power counting. To this end we employ the eigenfunctions of the NLO BFKL…
The high energy Operator Product Expansion for the product of two electromagnetic currents is extended to the sub-eikonal level in a rigorous way. I calculate the impact factors for polarized and unpolarized structure functions, define new…
The purpose of this paper is to give some refined results about the distribution of resonances in potential scattering. We use techniques and results from one and several complex variables, including properties of functions of completely…
A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach analytical expressions for elastic and inelastic scattering…
We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1 we…
This is a personal recollection of several results related to the study of the high energy limit of scattering amplitudes in gravitational theories. They would not have been possible without the encouragement and constant support from Lev…
We consider the cubic Schrodinger equation on the line, for which the scattering theory requires modifications due to long range effects. We revisit the construction of the modified wave operator, and recall the construction of its inverse,…
A method for the computation of scattering data and of the Green function for the one-dimensional Schr\"{o}dinger operator $H:=-\frac{d^2}{dx^2}+q(x)$ with a decaying potential is presented. It is based on representations for the Jost…