Clustering as a window on the hierarchical structure of quantum systems

Abstract Why do quantum particles form a hierarchical structure: quarks, hadrons, nuclei, atoms, and molecules? This is a fundamental question, and its answer is still elusive. Each hierarchical layer is characterized by the constituent particles, which are composite particles except for the quark hierarchy. Such a building block is regarded as a cluster and plays a role in forming a hierarchy. In the boundary of the neighboring hierarchies, we may find intermediate hierarchies, called semi-hierarchies , where a range of characteristic clusters, such as hadronic molecules, exotic hadrons, neutron halos, $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> clusters, and Feshbach molecules, appear. Such a cluster structure has some common features throughout the hierarchical layers with different scales. We discuss the role of clusters and their formation in semi-hierarchies.