Universality in Few-body Systems with Large Scattering Length

Details Universality in Few-body Systems with Large Scattering Length Universality in Few-body Systems with Large Scattering Length

2004-10-16

arxiv.org/abs/cond-mat/0410417v3

Phys.Rept.428:259-390,2006

Physics

Condensed Matter

Other Condensed Matter

219 pages, 58 figures, accepted for publication in Physics Reports, erroneous footnote on p. 200 removed

Scientific paper

10.1016/j.physrep.2006.03.001

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.

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