Entropy and complexity analysis of the D-dimensional rigid rotator and hyperspherical harmonics

TL;DR

This paper performs an information-theoretic analysis of the D-dimensional rigid rotator using entropy and complexity measures of hyperspherical harmonics, revealing the system's intricate geometric structure.

Contribution

It provides explicit expressions for entropic moments and Rényi entropies, advancing the understanding of complexity measures in high-dimensional quantum systems.

Findings

Explicit formulas for entropic moments and Rényi entropies.

Analysis of Fisher-Rényi, Fisher-Shannon, and LMC complexities.

Insights into the geometric complexity of D-dimensional hyperspherical harmonics.

Abstract

In this paper we carry out an information-theoretic analysis of the $D$-dimensional rigid rotator by studying the entropy and complexity measures of its wavefunctions, which are controlled by the hyperspherical harmonics. These measures quantify single and two-fold facets of the rich intrinsic structure of the system which are manifest by the intricate and complex variety of D-dimensional geometries of the hyperspherical harmonics. We calculate the explicit expressions of the entropic moments and the R\'enyi entropies as well as the Fisher-R\'enyi, Fisher-Shannon and LMC complexities of the system. The explicit expression for the last two complexity measures is not yet possible, mainly because the logarithmic functional of the Shannon entropy has not yet been obtained up until now in a closed for