Related papers: Dynamical versus diffraction spectrum for structur…
The diffraction spectrum of an aperiodic solid is related to the group of eigenvalues of the dynamical system associated with the solid. Those eigenvalues with continuous eigenfunctions constitute the topological Bragg spectrum. We relate…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
Many adaptive optics systems operate by measuring the distortion of the wavefront in one wavelength range and performing the scientific observations in a second, different wavelength range. One common technique is to measure wavefront…
In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital $C^*$-algebras, with a particular focus on gapped maps for…
There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
The characterization of dynamic phenomena using laser speckle has been studied in several applications and many descriptors have been developed to analyze the resulting images. In this work we compare the performance of a set of dynamic…
We show that ergodic dynamical systems generated by infinitely divisible stationary processes are disjoint in the sense of Furstenberg with distally simple systems and systems whose maximal spectral type is singular with respect to the…
We study deviation of ergodic averages for dynamical systems given by self-similar tilings on the plane and in higher dimensions. The main object of our paper is a special family of finitely-additive measures for our systems. An asymptotic…
Dynamic optical sensors, as those based on the reflectivity of isotropic dielectrical interfaces, can be useful for measuring small changes in the refractive index of fluid media. Exact and approximated explicit formulas for their…
A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The…
The spectral representation is an effecient tool to explore electrical properties of material mixtures. It separates the contributions of geometrical topology and intrinsic properties of the constituents in the system. The aim of this paper…
The article presents results of discrete thermodynamics (DTD) basic application to electrochemical systems. Consistent treatment of the electrochemical system as comprising two interacting subsystems - the chemical and the electrical…
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…
We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This…
We study totally ergodic quantum dynamical systems with quasi--discrete spectrum. We investigate the classification problem for such systems in terms of algebraic invariants. The results are noncommutative analogs of (a part of) the theory…
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…
We present results for the equilibrium statistics and dynamic evolution of moderately large ($n = {\mathcal{O}}(10^2 - 10^3)$) numbers of interacting point vortices on the unit sphere under the constraint of zero mean angular momentum. We…
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated…