Related papers: Which distributions of matter diffract? - Some ans…
We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project…
This paper considers some open questions related to the inverse problem of pure point diffraction, in particular, what types of objects may diffract, and which of these may exhibit the same diffraction. Some diverse objects with the same…
Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…
Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of…
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…
The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…
Diffuse scattering is usually associated with some disorder in the analyzed material. Different kinds of disorder may produce different diffuse scattering -- or not. In this letter, we demonstrate some aspects of the variety of diffuse…
There is a growing body of results in the theory of discrete point sets and tiling systems giving conditions under which such systems are pure point diffractive. Here we look at the opposite direction: what can we infer about a discrete…
Mathematical diffraction theory is concerned with the analysis of 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…
We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier.…
The presence of resonances modifies the passage of light or of electrons through a disordered medium. We generalize random matrix theory to account for this effect. Using supersymmetry, we calculate analytically the mean density of states,…
The disturbance of the transmission of light through a diffusive medium due to an object hidden in it can be expressed in terms of an effective charge and dipole moment. In the mesoscopic regime, beyond the diffusion approximation, we…
A potential scattering theory from deterministic and random $\mathcal{PT}$ collections of particles with gain and loss is introduced and the forms of their structure and pair-structure factors are elucidated. An example relating to light…
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sum of derivatives of generalized lattice…
We prove that the set of visible points of any lattice of dimension at least 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the…