Related papers: Information Entropy, Information Distances and Com…
Shannon entropy in position ($S_{\rvec}$) and momentum ($S_{\pvec}$) spaces, along with their sum ($S_t$) are presented for unit-normalized densities of He, Li$^+$ and Be$^{2+}$ ions, spatially confined at the center of an impenetrable…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
The general idea of information entropy provided by C.E. Shannon "hangs over everything we do" and can be applied to a great variety of problems once the connection between a distribution and the quantities of interest is found. The Shannon…
We calculate Shannon information entropy of trapped interacting bosons in both the position and momentum spaces, $S_r$ and $S_k$ respectively. The total entropy maintains the fuctional form $S=a + b \ln N$ for repulsive bosons. At the…
The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator…
A direct connection of information entropy $S$ and kinetic energy $T$ is obtained for nuclei and atomic clusters, which establishes $T$ as a measure of the information in a distribution. It is conjectured that this is a universal property…
In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and R\'enyi entropies, as descriptors of electronic correlation. By establishing a…
This contribution reviews a selection of findings on atomic density functions and discusses ways for reading chemical information from them. First an expression for the density function for atoms in the multi-configuration Hartree--Fock…
The information entropy of a nuclear density distribution is calculated for a number of nuclei. Various phenomenological models for the density distribution using different geometry are employed. Nuclear densities calculated within various…
In this chapter, a statistical measure of complexity and the Fisher-Shannon information product are introduced and their properties are discussed. These measures are based on the interplay between the Shannon information, or a function of…
We provide an algebraic procedure to find the eigenstates of two-charged particles in an oscillator potential, known as {\it{Hooke's}} atom. For the planar Hooke's atom, the exact eigenstates and single particle densities for arbitrary…
We consider Shannon entropy, Fisher information, R\'enyi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang…
In this study, the information-theoretic measures in both the position and momentum spaces for the pseudoharmonic potential using Fisher information, Shannon entropy, Renyi entropy, Tsallis entropy and Onicescu information energy are…
Information-based uncertainty measures like Shannon entropy, Onicescu energy and Fisher information (in position and momentum space) are employed to understand the effect of \emph{symmetric and asymmetric} confinement in a quantum harmonic…
We represent the two K-shell electrons of neutral atoms by Hylleraas-type wave function which fulfils the exact behavior at the electron-electron and electron-nucleus coalescence points and, derive a simple method to construct expressions…
The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms $H_c$, ${He_c}^+$ and ${Li_c}^{2+}$ confined by an impenetrable spherical box. Novel expressions for…
In information theory, one major goal is to find useful functions that summarize the amount of information contained in the interaction of several random variables. Specifically, one can ask how the classical Shannon entropy, mutual…
Information based uncertainty measures like R{\'e}nyi entropy (R), Shannon entropy (S) and Onicescu energy (E) (in both position and momentum space) are employed to understand the influence of radial confinement in isotropic harmonic…
The similarity of local atomic environments is an important concept in many machine-learning techniques which find applications in computational chemistry and material science. Here, we present and discuss a connection between the…
In this work, the calculation of complexity on atomic systems is considered. In order to unveil the increasing of this statistical magnitude with the atomic number due to the relativistic effects, recently reported in [A. Borgoo, F. De…