In this thesis nonrelativistic few-body quantum physics is investigated with the method of functional renormalization. In particular, we discuss different theoretical aspects of few-body physics related to the Efimov effect. Our central finding is that this effect manifests itself as a renormalization group limit cycle. First, we treat the problem of a singular, inverse square potential in quantum mechanics. Then we examine the original Efimov problem of three particles interacting via a short-range two-body potential. Subsequently, we present a first step towards the renormalization group solution of the four-body quantum problem for bosons. Finally, a general theoretical feature of the Efimov physics, composite operators with complex scaling dimensions, are discussed.
We study the semisuper-Efimov effect, which is found for four identical bosons with a resonant three-body interaction in 2D, in various systems. Based on solutions of bound-state and renormalization-group equations, we first demonstrate an emergence of the semisuper-Efimov effect in mass-imbalanced bosons in 2D. Compared with the Efimov and the super-Efimov effects, the mass ratio-dependent scaling parameter is unexpectedly found to take on a finite value even for extremely mass-imbalanced situations, where the mass ratio is 0 or
∞. By a renormalization-group analysis, we also show that a weak two-body interaction sustains the semisuper-Efimov effect. Finally, we liberate the universality of the semisuper-Efimov effect from 2D by showing that bosons with linear-dispersion relation support the semisuper-Efimov effect in 1D.
Efimov states represent a remarkable phenomenon in few‑body quantum physics in whichthree interacting particles can form a bound state even when none of the pairwiseinteractions are strong enough to bind the particles independently. An especially notableproperty of Efimov systems is discrete scale invariance: if one Efimov bound state exists,additional bound states can appear at larger spatial scales following a fixed scaling ratio.This paper examines the conceptual relevance of Efimov states to the SP3 (space‑phase)framework, which proposes that matter–energy transport can condition the spacetimesubstrate and form persistent transport pathways known as coherence corridors. Withinthis interpretation, Efimov physics provides a quantum‑scale example of hierarchical,threshold‑dependent organization in which collective interactions produce stablestructures that repeat across scale. The analogy suggests that node accumulation andrelease processes in SP3 transport networks may share structural similarities withhierarchical binding phenomena observed in Efimov systems.