相关论文: Scaling of the Thue-Morse diffraction measure
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…
We present a new measure of the Dynamical Critical behavior: the "Multi-scale Dynamical Exponent (MDE)"
Complex signed measures of finite total variation are a powerful signal model in many applications. Restricting to the $d$-dimensional torus, finitely supported measures allow for exact recovery if the trigonometric moments up to some order…
We apply the supersymmetric Darboux transformation to the optical Helmoltz wave equation to generate analytically complex-valued PT-symmetric potentials (physically a graded refractive index dielectric). PT-symmetry is then spontaneously…
We consider rank one measure preserving transformations $g$ and the corresponding unitary operators $U(g)$. It is known that a generic (in the sense of Baire category) measure preserving transformation has rank one, spectral type of $U(g)$…
We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant.
The nonlinear properties of quasiperiodic photonic crystals based on the Thue-Morse sequence are investigated. The intrinsic spatial asymmetry of these one-dimensional structures for odd generation numbers results in bistability thresholds…
We extend a recent result of Burns, Guillemin and Uribe on the asymptotics of the spectral measure for the reduction metric on a toric variety to any toric metric on a toric variety. We show how this extended result together with the…
Transmission matrices are valuable tools to describe and control light transport through scattering media. There are only a few cases where the transmission matrix can be compared to microscopic theories. Here we measure the…
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…
We present an improved scheme for the precise evaluation of finite-temperature response functions of strongly correlated systems in the framework of the time-dependent density matrix renormalization group. The maximum times that we can…
We prove that a positive-definite measure in $\mathbb{R}^n$ with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent…
We compute the equilibrium measure in dimension d=s+4 associated to a Riesz s-kernel interaction with an external field given by a power of the Euclidean norm. Our study reveals that the equilibrium measure can be a mixture of a continuous…
The Thue-Morse sequence is an aperiodically ordered infinite binary sequence. It is used as a one-dimensional way to model the structure of a quasicrystal. For example, taking autocorrelations of these sequences (roughly, measuring how…
We study the effect of a finite sample size, beam divergence and detector thickness on the resolution function of a MIEZE spectrometer. We provide a transparent analytical framework which can be used to determine the optimal trade-off…
An integral representation result for strictly positive subharmonic functions of a one-dimensional regular diffusion is established. More precisely, any such function can be written as a linear combination of an increasing and a decreasing…
As a guiding example, the diffraction measure of a random local mixture of the two classic Fibonacci substitutions is determined and reanalysed via self-similar measures of Hutchinson type, defined by a finite family of contractions. Our…
We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of the hyperbolic plane we can interpret the spherical…
We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using…
We give a Herglotz-type representation of an arbitrary generalized spectral measure. As an application, a new proof of the classical Naimark's dilation theorem is given. The same approach is used to describe the spectrum of all unitary…