Arrangement and chemical complexity in an $N$-body quantum system

TL;DR

This paper introduces the concept of arrangement in $N$-body quantum systems, linking particle attraction and binding to system complexity, and explores its role in understanding energy spectra and multiparticle separability.

Contribution

It extends the concept of arrangement from chemical reactions to general $N$-body quantum systems, providing a new framework for analyzing their structure and spectra.

Findings

Arrangement is essential for characterizing quantum states.

Arrangement relates to the energy spectrum structure.

Multiparticle separability is formulated mathematically.

Abstract

We introduce and discuss the concept of \textit{arrangement}, traditionally found in the context of chemical reactions and few-body rearrangement collisions, in the general context of an $N$-body quantum system. We show that the ability for particles to attract and bind is a key source of complexity of an $N$-body quantum system, and \textit{arrangement} is an emergent concept necessitated by the description of this complexity. For an $N$-body system made of particles of which some or all can attract and bind, the concept of arrangement is not only necessary for a full characterization of its quantum states and processes, but it also provides a basis for the understanding and the description of the structure of its energy spectrum. We also discuss and formulate multiparticle separability in an $N$-body system, the mathematical foundation that underlies the arrangement concept in an $N$-body theory.