Charged analogs of the Efimov effect

Yunfei Xue, Jiabin Wang, Li Chen +2 more

Efimov effects arise from scale invariance, a fundamental symmetry with universal implications. While spatial Efimov physics has been extensively studied, realizing its temporal counterpart remains challenging, as it requires a dynamical system that breaks time-translation symmetry yet preserves the essential time-scaling symmetry. Analog cosmology offers a powerful platform to address this challenge, bridging the domains of Efimov physics and cosmology. Here, we predict a temporal Efimov effect in an analog linearly expanding universe realized with a quasi-two-dimensional Bose-Einstein condensate. The invariance of phonon mode equations under time rescaling leads to particle production with two distinct dynamics: power-law growth and log-periodic oscillations, with the latter being the hallmark signature of the Efimov effect. Furthermore, these dynamics map directly onto sub- and super-horizon cosmological modes. Our predictions can be directly verified through time-averaged measurements of the density-fluctuation spectrum $S_{k}(t)$ in current experiments.

A. C. Fonseca, Edward F. Redish, Paul E. Shanley

Syed Muntasir Mamun

The Efimov effect represents a cornerstone of quantum few-body physics, manifesting as an infinite sequence of weakly bound three-body states in systems with resonant pairwise interactions. This paper introduces a novel conceptual framework by analogizing this quantum phenomenon to classical geometric triangulation in infinite Euclidean space. By conceptualizing three interconnected points as a self-referential structure that imposes coordinates in a featureless infinity, we elucidate how relative configurations enable binding and scaling in scale-invariant systems. The innovation lies in this relational geometric "mock-up," which demystifies the discrete scaling of Efimov trimers, offering a pedagogical bridge between classical geometry and quantum universality. We provide rigorous derivations of the Efimov effect, including an expanded treatment of hyperspherical coordinates, alongside extensions of the analogy to 3D trilateration. This approach not only enhances educational accessibility but also inspires interdisciplinary insights into emergent structures in infinite spaces. Also available on Academia.edu: https://www.academia.edu/attachments/129096461/download_file?s=portfolio

Lucas Platter

Jonathan Rau, Marvin R. Schulz

We prove that the Schrödinger operator describing four particles in two dimensions, interacting solely through short-range three-body forces, can possess infinitely many bound states. This holds under the assumption that each three-body subsystem has a virtual level at zero energy. Our result establishes an analog of the Efimov effect for such four-particle systems in two dimensions.

Miwae Yamazaki