Universality in Few-body Systems with Large Scattering Length

TL;DR

This paper reviews the universal properties of few-body systems with large scattering lengths, focusing on Efimov states in three-boson systems and extending the discussion to more complex systems using various theoretical tools.

Contribution

It provides a comprehensive review of universality in few-body systems, emphasizing Efimov physics and the application of hyperspherical formalism, Efimov's radial laws, and effective field theory.

Findings

Efimov states exhibit discrete scaling symmetry at large scattering lengths

Universal relations hold for three-boson systems regardless of short-range details

Extensions to systems with more particles are discussed

Abstract

Particles with short-range interactions and a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-body sector, the universal properties are familiar and depend only on the scattering length a. In the 3-body sector for identical bosons, the universal properties include the existence of a sequence of shallow 3-body bound states called "Efimov states" and log-periodic dependence of scattering observables on the energy and the scattering length. The spectrum of Efimov states in the limit a -> +/- infinity is characterized by an asymptotic discrete scaling symmetry that is the signature of renormalization group flow to a limit cycle. In this review, we present a thorough treatment of universality for the system of three identical bosons and we summarize the universal information that is currently available for other 3-body systems. Our basic tools are the hyperspherical formalism to provide qualitative insights, Efimov's radial laws for deriving the constraints from unitarity, and effective field theory for quantitative calculations. We also discuss topics on the frontiers of universality, including its extension to systems with four or more particles and the systematic calculation of deviations from universality.