Related papers: Information-theoretic-based spreading measures of …
The Renyi, Shannon and Fisher spreading lengths of the classical or hypergeometric orthogonal polynomials, which are quantifiers of their distribution all over the orthogonality interval, are defined and investigated. These…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like…
The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…
The main monotonic statistical complexity-like measures of the Rakhmanov's probability density associated to the hypergeometric orthogonal polynomials (HOPs) in a real continuous variable, each of them quantifying two configurational facets…
In this work, the probability uncertainties related to a stationary quantum system with solitonic mass distribution when subjected to deformable hyperbolic potentials are studied. Shannon's entropy and Fisher's information of a…
The direct spreading measures of the Laguerre polynomials, which quantify the distribution of its Rakhmanov probability density along the positive real line in various complementary and qualitatively different ways, are investigated. These…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…
The position and momentum spreading of the electron distribution of the two-dimensional confined hydrogenic atom, which is a basic prototype of the general multidimensional confined quantum systems, is numerically studied in terms of the…
The internal disorder of hydrogenic Rydberg atoms as contained in their position and momentum probability densities is examined by means of the following information-theoretic spreading quantities: the radial and logarithmic expectation…
The analytic information theory of discrete distributions was initiated in 1998 by C. Knessl, P. Jacquet and S. Szpankowski who addressed the precise evaluation of the Renyi and Shannon entropies of the Poisson, Pascal (or negative…
Orthogonal polynomials with respect to the hypergeometric distribution on lattices in polyhedral domains in ${\mathbb R}^d$, which include hexagons in ${\mathbb R}^2$ and truncated tetrahedrons in ${\mathbb R}^3$, are defined and studied.…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
The determination of the physical entropies (R\'enyi, Shannon, Tsallis) of high-dimensional quantum systems subject to a central potential requires the knowledge of the asymptotics of some power and logarithmic integral functionals of the…
Using entropic inequalities for Shannon entropies new inequalities for some classical polynomials are obtained. To this end, photon distribution functions for one-, two- and multi-mode squeezed states in terms of Hermite, Laguerre, Legendre…
A family of orthogonal polynomials on the disk (which we call scattering polynomials) serves to formulate a remarkable Fourier expansion of the composition of a sequence of Poincar\'e disk automorphisms. Scattering polynomials are tied to…
Shannon quantum information entropies $S_{\rho,\gamma}$, Fisher informations $I_{\rho,\gamma}$, Onicescu energies $O_{\rho,\gamma}$ and complexities $e^SO$ are calculated both in position (subscript $\rho$) and momentum ($\gamma$) spaces…
The fundamental information-theoretic measures (the R\'enyi $R_{p}[\rho]$ and Tsallis $T_{p}[\rho]$ entropies, $p>0$) of the highly-excited (Rydberg) quantum states of the $D$-dimensional ($D>1$) hydrogenic systems, which include the…
Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion. Multi-indexed orthogonal polynomials are labeled…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…