Few-Body Effects in Cold Atoms and Limit Cycles

TL;DR

This paper reviews the universal properties of systems with large scattering lengths, focusing on Efimov states and limit cycles, with applications to cold atom experiments and connections to nuclear physics.

Contribution

It provides an overview of universality in few-body systems, emphasizing the role of limit cycles and discussing recent developments in cold atom applications.

Findings

Universal three-body bound states (Efimov states) exhibit geometric spectra.

Low-energy observables show log-periodic dependence on system parameters.

Universality extends to four-body systems and beyond.

Abstract

Physical systems with a large scattering length have universal properties independent of the details of the interaction at short distances. Such systems can be realized in experiments with cold atoms close to a Feshbach resonance. They also occur in many other areas of physics such as nuclear and particle physics. The universal properties include a geometric spectrum of three-body bound states (so-called Efimov states) and log-periodic dependence of low-energy observables on the physical parameters of the system. This behavior is characteristic of a renormalization group limit cycle. We discuss universality in the three- and four-body sectors and give an overview of applications in cold atoms.