Related papers: Substitution-based sequences with absolutely conti…
The primary objective of this paper is to generalize the results of [arXiv:2111.03548] to the case of quasi-smooth Berkovich curves by establishing a connection between the spectrum and the radii of convergence. To achieve this, we…
By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d.\ sequences. This observation not only explains the remarkable properties of lacunary trigonometric…
We holographically compute supercharge diffusion constants in supersymmetric field theories, dual to AdS black brane solutions of arbitrary dimension. This includes the extension of earlier work by Kontoudi and Policastro for D3-branes to…
Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional…
This paper is a review containing new original results on the finite order variational sequence and its different representations with emphasis on applications in the theory of variational symmetries and conservation laws in physics.
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these…
Recently, Differentiable Ray Tracing has been successfully applied in the field of wireless communications for learning radio materials or optimizing the transmitter orientation. However, in the frame of gradient based optimization,…
We introduce a procedure for establishing pure discrete spectrum for substitution tiling systems of Pisot family type and illustrate with several examples.
Consider the problem of scattering of electromagnetic waves by a doubly periodic structure. The medium above the structure is assumed to be inhomogeneous characterized completely by an index of refraction. Below the structure is a perfect…
For lossless periodic structures with a proper symmetry, the transmission and reflection spectra often have peaks and dips that are truly $100\%$ and $0\%$, respectively. The full peaks and zero dips typically appear near resonant…
Based on the classical Lorentz model of the index of refraction, a new method is presented for the extraction of the complex index of refraction from the extinction efficiency of homogeneous and layered dielectric spheres that…
A class of one-dimensional reflectionless potentials, an absolute transparency of which is concerned with their belonging to one SUSY-hierarchy with a constant potential, is studied. An approach for determination of a general form of the…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explicit construction of a fundamental domain with fractal…
It is shown that for any family of probability measures in Ornstein type constructions the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem, the same result is proved for…
The paper investigates how correlations can completely specify a uniformly discrete point process. The setting is that of uniformly discrete point sets in real space for which the corresponding dynamical hull is ergodic. The first result is…
The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in $\{\pm 1\}$. We revisit this example and derive a…
We characterize the absolutely continuous spectrum of half-line one-dimensional Schr\"odinger operators in terms of the limiting behavior of the Crystaline Landauer-B\"uttiker conductance of the associated finite samples.
We introduce several new constructions for perfect periodic autocorrelation sequences and arrays over the unit quaternions. This paper uses both mathematical proofs and com- puter experiments to prove the (bounded) array constructions have…