Related papers: Quasicrystals with discrete support and spectrum

It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular,…

In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that,…

We prove that supports of a wide class of temperate distributions with uniformly discrete support and spectrum on Euclidean spaces are finite unions of translations of full-rank lattices. This result is a generalization of the corresponding…

We prove that there is a structure, indeed a linear ordering, whose degree spectrum is the set of all non-hyperarithmetic degrees. We also show that degree spectra can distinguish measure from category.

We study a certain family of discrete measures with unit masses on a horizontal strip as an analogue of Fourier quasicrystals on the real line. We prove a one-to-one correspondence between supports of measures from this family and zero sets…

We construct a function on the real line supported on a set of finite measure whose spectrum has density zero.

The ${q}\bar{q}$ spectrum is studied within a chiral constituent quark model. It provides with a good fit of the available experimental data from light (vector and pseudoscalar) to heavy mesons including some recent results on charmonium.…

In this paper we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed curves to be…

We present a brief history of quasicrystals and a short introduction to classical lattice-gas models of interacting particles. We discuss stability of non-periodic tilings and one-dimensional sequences of symbols seen as ground states of…

We prove that projectivised finite-dimensional linear random dynamical systems possess a unique finest weak Morse decomposition. Based on this result, we define the Morse spectrum and investigate its basic properties. In particular, we show…

A discrete set in the Euclidian space is almost periodic, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We prove the following result: if A is a discrete almost periodic set and the set A-A…

Due to their aperiodic nature, quasicrystals are one of the least understood phases in statistical physics. One significant complication they present in comparison to their periodic counterparts is the fact that any quasicrystal can be…

Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under…

We prove that each discrete set in the Euclidean space that has bounded changes under every translation is a bounded perturbation of a square lattice, i.e., a uniformly spread set in the sense of Laszkovich. In particular, the support of…

We study the point spectrum of a periodic quantum tree equipped with a Schr\"odinger type differential operator with delta-type vertex conditions, using subsets of the compact graph that generates the tree. We prove analogs of existing…

Motivated by recent interest in the spectrum of the Laplacian of incomplete surfaces with isolated conical singularities, we consider more general incomplete m-dimensional manifolds with singularities on sets of codimension at least 2. With…

Quasiperiodic tilings are often considered as structure models of quasicrystals. In this context, it is important to study the nature of the diffraction measures for tilings. In this article, we investigate the diffraction measures for…

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…

In this paper we investigate the problems related to measures with a natural spectrum (equal to the closure of the set of the values of the Fourier-Stieltjes transform). Since it is known that the set of all such measures does not have a…

We study spectral synthesis for measures supported on thin subsets of compact Riemannian manifolds. We prove that under natural non-concentration conditions, such measures admit quantitative spectral synthesis, with explicit stability…