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.
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.
The Efimov phenomenon manifests itself as an emergent discrete scaling symmetry in the quantum three-body problem. In the unitarity limit, it leads to an infinite tower of three-body bound states with energies forming a geometric sequence. In this work, we study the evolution of these so-called Efimov states using relativistic scattering theory. We identify them as poles of the three-particle S matrix in the complex energy plane, and we study how they transform from virtual states through bound states to resonances when we change the interaction strength. We dial the scattering parameters toward the unitarity limit and observe the emergence of the universal scaling of energies and couplings---a behavior known from the nonrelativistic case. We additionally find that Efimov resonances follow unusual, cyclic trajectories accumulating at the three-body threshold and then disappear at some values of the two-body scattering length. We propose a partial resolution to this ``missing states'' problem.
The Efimov states are three-body bound states, which appear universally when the s-wave scattering length between the particles is resonantly large.Since the Efimov states and their characteristic discrete scale invariance have recently been observed in ultracold atoms, the Efimov states and their associated few-body phenomena have attracted widening interest both theoretically and experimentally.In this thesis, I theoretically study the Efimov physics and related phenomena, focusing on the following three topics: (i) Universal three-body physics for a mass-imbalanced Fermi system (Chapter 3).For a system of two identical spinless (i.e., spin-polarized) fermions and one distinguishable particle which interact via a short-range potential with a large s-wave scattering length, two classes of universal three-body bound states have been known to appear in different regimes of the mass ratio: the Efimov trimers and the Kartavtsev-Malykh trimers, which feature the discrete and continuous scale invariance, respectively.I have found the third class of universal three-body bound states, which I call the "crossover trimers".The crossover trimers show neither the discrete nor continuous scale invariance.I have identified the regions of these three classes of trimers as a function of the mass ratio and the s-wave scattering length, and shown that the Kartavtsev-Malykh trimers and the Efimov trimers can continuously transform into each other via the crossover trimers as the mass ratio and the s-wave scattering length are varied.Owing to the presence of the crossover trimers, the Kartavtsev-Malykh trimers dissociate into a particle and a dimer when the s-wave scattering length is varied, inducing resonances in the particle-dimer scattering.I have calculated the elastic particle-dimer scattering lengths in arbitrary angular-momentum channels, and shown that the particle-dimer resonances indeed occur.From the resonance positions, I have found accurate values of the critical mass ratios at which the Kartavtsev-Malykh trimers in the higher angular-momentum channels appear. (ii) Universal three-body parameter (Chapter 4).In the Efimov physics, the three-body parameter fixes the short-range three-body phase and hence the scale of the energy spectrum.Until quite recently, it has been widely held that the threebody parameter should depend on the short-range part of the inter-atomic potential, and hence vary almost randomly between different atomic species and hyperfine states.However, mounting evidence in recent experiments suggests otherwise.While some theoretical studies have succeeded in reproducing the universal behavior in the three-body parameter, the underlying physical mechanism has remained unclear and controversial.In this thesis, I elucidate the physical origin of the universal three-body parameter.I propose that a non-adiabatic deformation of the three-body wave function induced by a universal two-body correlation results in a universal three-body repulsion, which prevents three particles from coming close and renders the three-body parameter universal.This mechanism is verified by reproducing the universal three-body repulsion with a simple model wave function.The mechanism found here suggests that the three-body parameter would also be universal for non-van der Waals types of potentials.For various classes of deep two-body potentials, it is shown that the effective range is the relevant length scale to characterize the two-body correlation and sets the three-body parameter.Depending on the shape of the two-body correlation, there
Nature appears to employ selective exchange mechanisms at every observable scale.Rather than permitting unrestricted transfer of energy, matter, momentum, charge, orinformation, many systems utilize highly constrained corridors through which exchangeoccurs while organizational stability is preserved. This paper examines several quantumphenomena—including quantum tunneling, atomic transitions, Josephson junctions,photonic waveguides, and quantum information channels—as examples of what may betermed Selective Exchange Corridors (SECs).A common architectural pattern is identified consisting of four elements: a sourcereservoir, a transport corridor, a threshold-regulated exchange region, and a receivingreservoir. Although the governing mathematics differs among systems, the recurringorganizational structure appears remarkably consistent. The analysis then extends tolarger-scale examples including biological transport systems, planetary magnetospheres,spiral galaxies, and cosmic filaments. Within the SP3 framework, this recurrence isinterpreted as evidence that regulated exchange represents a fundamental organizationalprinciple of reality rather than an isolated characteristic of particular physical systems.
Nature appears to employ selective exchange mechanisms at every observable scale.Rather than permitting unrestricted transfer of energy, matter, momentum, charge, orinformation, many systems utilize highly constrained corridors through which exchangeoccurs while organizational stability is preserved. This paper examines several quantumphenomena—including quantum tunneling, atomic transitions, Josephson junctions,photonic waveguides, and quantum information channels—as examples of what may betermed Selective Exchange Corridors (SECs).A common architectural pattern is identified consisting of four elements: a sourcereservoir, a transport corridor, a threshold-regulated exchange region, and a receivingreservoir. Although the governing mathematics differs among systems, the recurringorganizational structure appears remarkably consistent. The analysis then extends tolarger-scale examples including biological transport systems, planetary magnetospheres,spiral galaxies, and cosmic filaments. Within the SP3 framework, this recurrence isinterpreted as evidence that regulated exchange represents a fundamental organizationalprinciple of reality rather than an isolated characteristic of particular physical systems.
Efimov states are known to have a discrete real-space scale invariance; working in momentum space we identify the relevant discrete scale invariance for the scattering amplitude defining its Weierstrass function as well. Through the use of the mathematical formalism for discrete scale invariance for the scattering amplitude we identify the scaling parameters from the pole structure of the corresponding zeta function; its zeroth-order pole is fixed by the Efimov physics. The corresponding geometrical fractal structure for Efimov physics in momentum space is identified as a ray across a logarithmic spiral. This geometrical structure also appears in the physics of atomic collapse in the relativistic regime connecting it to Efimov physics. Transforming to logarithmic variables in momentum space we map the three-body scattering amplitude into Bloch states and the ladder of energies of the Efimov states are simply obtained in terms of the Bohr-Sommerfeld quantization rule. Thus through the mapping the complex problem of three-body short-range interaction is transformed to that of a noninteracting single particle in a discrete lattice.
Universal behavior has been found inside the window of Efimov physics for systems with N=4,5,6 particles. Efimov physics refers to the emergence of a number of three-body states in systems of identical bosons interacting via a short-range interaction becoming infinite at the verge of binding two particles. These Efimov states display a discrete scale invariance symmetry, with the scaling factor independent of the microscopic interaction. Their energies in the limit of zero-range interaction can be parametrized, as a function of the scattering length, by a universal function. We have found, using the form of finite-range scaling introduced by A. Kievsky and M. Gattobigio [Phys. Rev A 87, 052719 (2013)], that the same universal function can be used to parametrize the ground and excited energy of $N\ensuremath{\le}6$ systems inside the Efimov-physics window. Moreover, we show that the same finite-scale analysis reconciles experimental measurements of three-body binding energies with the universal theory.