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It is well known that a hyperbolic domain in the complex plane has uniformly perfect boundary precisely when the product of its hyperbolic density and the distance function to its boundary has a positive lower bound. We extend this…
Single-photon transitions are one of the key technologies for designing and operating very-long-baseline atom interferometers tailored for terrestrial gravitational-wave and dark-matter detection. Since such setups aim at the detection of…
A method is proposed for the calculation of diffusion constants for one-dimensional maps exhibiting deterministic diffusion. The procedure is based on harmonic inversion and uses a known relation between the diffusion constant and the…
Spectral densities connect correlation functions computed in quantum field theory to observables measured in experiments. For strongly-interacting theories, their non-perturbative determinations from lattice simulations are therefore of…
Kirchhoff's scalar diffraction theory is applied throughout photon and electron optics. It is based on the stationary electromagnetic or Schr\"odinger wave equation, and is useful in describing interference phenomena for both light and…
The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the…
Very short pulses of x-ray free-electron lasers opened the way to obtain diffraction signal from single particles beyond the radiation dose limit. For 3D structure reconstruction many patterns are recorded in the object's unknown…
Regular model sets, describing the point positions of ideal quasicrystallographic tilings, are mathematical models of quasicrystals. An important result in mathematical diffraction theory of regular model sets, which are defined on locally…
We obtain new inversion formulas for the Funk type transforms of two kinds associated to spherical sections by hyperplanes passing through a common point $A$ which lies inside the n-dimensional unit sphere or on the sphere itself.…
Scattering amplitudes are tempered distributions, which are defined through their action on functions in the Schwartz space $S(\mathbb{R})$ by duality. For massless particles, their conformal properties become manifest when considering…
I propose that the proper framework for gravitational scattering theory is the rep- resentation theory of the super-BMS algebra of Awada, Gibbons and Shaw[1], and its generalizations. Certain representation spaces of these algebras…
Is there a translation-bounded measure whose diffraction is spherically symmetric and concentrated on a single sphere? This note constructively answers this question of Strungaru in the affirmative.
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…
We consider consistent diffusion dynamics, leaving the celebrated Hua-Pickrell measures, depending on a complex parameter $s$, invariant. These, give rise to Feller-Markov processes on the infinite dimensional boundary $\Omega$ of the…
Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…
We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…
Deterministic control of coherent random light is highly important for information transmission through complex media. However, only a few simple speckle transformations can be achieved through diffusers without prior characterization. As…
We derive explicit formulas for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulas are important for problems of thermo- and photo-…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
In absence of a lens to form an image, incoherent or partially coherent light scattering off an obstructive or reflective object forms a broad intensity distribution in the far field with only feeble spatial features. We show here that…