Complexity classification of quantum many-body systems according to the Pair of Order-Disorder Indices (PODI)

TL;DR

This paper introduces the Pair of Order-Disorder Indices (PODI) as a new way to classify the complexity of quantum many-body systems, revealing distinct order or disorder characteristics across different systems and implications for their growth in complexity.

Contribution

The study proposes a novel classification method using complexity measures to quantify order and disorder in quantum systems, extending to classical systems and analyzing complexity growth with particle number.

Findings

Atoms are characterized by order and self-organization.

Bosons exhibit disorder in their complexity profile.

Nuclei and atomic clusters are less disordered than bosons.

Abstract

The statistical measures of complexity defined by Lopez-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison and Landsberg (SDL) are calculated as functions of the number of particles for four quantum many-body systems, i.e. atoms, nuclei, atomic clusters, and correlated atoms in a trap (bosons). A pair of order and disorder strengths, evaluated for each system, can serve as a Pair of Order-Disorder Indices (PODI), characterizing quantitatively order versus disorder in any quantum system. According to the above classification, we assign to bosons the complexity character of disorder, to atoms the character of order, while nuclei and atomic clusters are (less) disordered and lie between them. This criterion can be used to estimate the relative contribution of order and disorder to complexity for other more complicated quantum systems as well and even classical ones, if one is able to describe them probabilistically. We also address the issue, whether those systems can grow in complexity as the number of particles increases. Our comparative study indicates that atoms are the only quantum system out of four, which is ordered, with the ability to self-organize. We conjecture that this is an information-theoretic reason that atoms are suitable as building blocks of larger structures of biological interest i.e. molecules and macromolecules. This is in the spirit of Wheeler's "it from bit" quote, the project to present everything about the Universe in terms of information theory.