Higher-order Brunnian structures and possible physical realizations

TL;DR

This paper explores higher-order Brunnian structures in few-body systems, discussing their mathematical foundations and potential physical realizations in nuclei, cold atoms, and condensed matter, emphasizing the need for specific interaction conditions.

Contribution

It introduces the concept of higher-order Brunnian structures in physical systems and analyzes their potential realizations across various fields.

Findings

Higher-order Brunnian structures can potentially be realized in laboratory or natural systems.

Cold atoms are promising for realizing these structures due to controllable interactions.

Nuclear realization is unlikely without luck due to fixed interaction strengths.

Abstract

We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of systems in nature. It now appears that recent generalization to higher order Brunnian structures may potentially be realized as laboratory made or naturally occurring systems. With the binding energy as measure, we discuss possibilities of physical realization in nuclei, cold atoms, and condensed matter systems. Appearance is not excluded. However, both the form and the strengths of the interactions must be rather special. The most promising subfields for present searches would be in cold atoms because of external control of effective interactions, or perhaps in condensed-matter systems with non-local interactions. In nuclei, it would only be by sheer luck due to a lack of tunability.