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A new correlation measure, the product of the Shannon entropy power and the Fisher information of the electron density, is introduced by analyzing the Fisher-Shannon information plane of some two-electron systems (He-like ions, Hooke's atoms). The uncertainty and scaling properties of this information product are pointed out. In addition, the Fisher and… (More)

- E Romera, J C Angulo, J S Dehesa
- 2001

Our aim in this paper is twofold. First, to find the necessary and sufficient conditions to be satisfied by a given sequence of real numbers ͕ n ͖ nϭ0 ϱ to represent the ''entropic moments'' ͐ [0,a] ͓(x)͔ n dx of an unknown non-negative, decreasing and differentiable ͑a.e.͒ density function (x) with a finite interval support. These moments are called… (More)

- E Romera, J C Angulo, J S Dehesa
- 1999

General model-independent relationships among radial expectation values of the one-particle densities in position and momentum spaces for any quantum-mechanical system are obtained. They are derived from the Stam uncertainty principle and the recently reported lower bounds to the Fisher information entropy of both densities. The results are usually… (More)

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 it, and the separation of the set of accessible states to a system from the equiprob-ability distribution, i.e. the… (More)

A two-parameter family of complexity measures C ˜ ͑␣,͒ based on the Rényi entro-pies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the Lopez-Ruiz– Mancini–Calbet complexity, which is recovered for ␣ = 1 and  = 2. These complexity measures are obtained by… (More)

- E Romera
- 2002

Several D-dimensional uncertainty-like relationships for N-body systems are obtained by means of the Fisher's information entropies in position and momentum spaces and the Stam's uncertainty principle. In addition, these relationships, the Fisher's entropies and the Stam's inequality are analysed numerically for all ground state neutral atoms from hydrogen… (More)

- J C Angulo, E Romera, J S Dehesa
- 2000

Rigorous relationships among physically relevant quantities of atomic systems ͑e.g., kinetic, exchange, and electron–nucleus attraction energies, information en-tropy͒ are obtained and numerically analyzed. They are based on the properties of inverse functions associated to the one-particle density of the system. Some of the new inequalities are of great… (More)

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 it, and the separation of the set of accessible states to a system from the equiprobability distribution, i.e. the… (More)

The concept of Fisher-Shannon information plane, defined by the Fisher information I and the Shannon entropy H of the one-particle distribution density, is proposed as a new tool to analyze the internal disorder of complex systems as well as to disentangle between their spectra regimes. The former is illustrated for various members of the He-like… (More)

Structural characteristics of the spherically averaged internally folded density or reciprocal form factor Br are studied within the Hartree-Fock framework for 103 neutral atoms, 54 singly charged cations, and 43 anions in their ground state. The function Br is classified throughout the Periodic Table into three types: (i) monotonic decrease from the… (More)

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