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

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.