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Title: Information-theoretic measures of hyperspherical harmonics

Abstract

The multidimensional spreading of the hyperspherical harmonics can be measured in a different and complementary manner by means of the following information-theoretic quantities: the Fisher information, the average density or first-order entropic moment, and the Shannon entropy. They give measures of the volume anisotropy of the eigenfunctions of any central potential in the hyperspace. Contrary to the Fisher information, which is a local measure because of its gradient-functional form, the other two quantities have a global character because they are powerlike (average density) and logarithmic (Shannon's entropy) functionals of the hyperspherical harmonics. In this paper we obtain the explicit expression of the first two measures and a lower bound to the Shannon entropy in terms of the labeling indices of the hyperspherical harmonics.

Authors:
; ;  [1];  [2]
  1. Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071 Granada (Spain) and Departamento de Fisica Moderna, Universidad de Granada, 18071 Granada (Spain)
  2. (Spain) and Departamento de Matematica Aplicada, Universidad de Granada, 18071 Granada (Spain)
Publication Date:
OSTI Identifier:
20929685
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 4; Other Information: DOI: 10.1063/1.2712913; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; CENTRAL POTENTIAL; EIGENFUNCTIONS; ENTROPY; FUNCTIONAL ANALYSIS; SPHERICAL HARMONICS

Citation Formats

Dehesa, J. S., Lopez-Rosa, S., Yanez, R. J., and Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071 Granada. Information-theoretic measures of hyperspherical harmonics. United States: N. p., 2007. Web. doi:10.1063/1.2712913.
Dehesa, J. S., Lopez-Rosa, S., Yanez, R. J., & Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071 Granada. Information-theoretic measures of hyperspherical harmonics. United States. doi:10.1063/1.2712913.
Dehesa, J. S., Lopez-Rosa, S., Yanez, R. J., and Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071 Granada. Sun . "Information-theoretic measures of hyperspherical harmonics". United States. doi:10.1063/1.2712913.
@article{osti_20929685,
title = {Information-theoretic measures of hyperspherical harmonics},
author = {Dehesa, J. S. and Lopez-Rosa, S. and Yanez, R. J. and Instituto Carlos I de Fisica Teorica y Computacional, Universidad de Granada, 18071 Granada},
abstractNote = {The multidimensional spreading of the hyperspherical harmonics can be measured in a different and complementary manner by means of the following information-theoretic quantities: the Fisher information, the average density or first-order entropic moment, and the Shannon entropy. They give measures of the volume anisotropy of the eigenfunctions of any central potential in the hyperspace. Contrary to the Fisher information, which is a local measure because of its gradient-functional form, the other two quantities have a global character because they are powerlike (average density) and logarithmic (Shannon's entropy) functionals of the hyperspherical harmonics. In this paper we obtain the explicit expression of the first two measures and a lower bound to the Shannon entropy in terms of the labeling indices of the hyperspherical harmonics.},
doi = {10.1063/1.2712913},
journal = {Journal of Mathematical Physics},
number = 4,
volume = 48,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}