Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of ${}^{4}\mathrm{He}$ atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.Efimov states are a sequence of shallow three-body bound states that arise when the two-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a three-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of ${}^{4}\mathrm{He}$ atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.

arXiv:cond-mat/0201281Physical Review AFeb 28, 200354 citations

The Efimov effect in a four-body system

H. W. L. Naus, John A. Tjon

Few-Body SystemsJan 1, 198715 citations

Three- and four-body systems with the Functional Renormalization Group

Benjamín Raziel, Benjamín Raziel Jaramillo Avila

The Efimov effect arises in three-body systems near the unitary limit. Some of its features are universal, while others are not. This article uses a Functional-Renormalization- Group approach to discuss the Efimov effect and four-body systems. In this context, the Efimov effect appears as a consequence of the Renormalization-Group flow of couplings. On the four- body system, we find three tetramers below each Efimov trimer, and no evidence of four- body universality breaking. Two of these tetramers are in agreement with quantum-mechanical calculations and experimental results.The Efimov effect arises in three-body systems near the unitary limit. Some of its features are universal, while others are not. This article uses a Functional-Renormalization- Group approach to discuss the Efimov effect and four-body systems. In this context, the Efimov effect appears as a consequence of the Renormalization-Group flow of couplings. On the four- body system, we find three tetramers below each Efimov trimer, and no evidence of four- body universality breaking. Two of these tetramers are in agreement with quantum-mechanical calculations and experimental results.

Journal of Physics Conference SeriesOct 1, 20160 citations

Origin of the Three-Body Parameter Universality in Efimov Physics

Jia Wang, José Paulo D'Incao, Brett D. Esry +1 more

In recent years extensive theoretical and experimental studies of universal few-body physics have advanced our understanding of universal Efimov physics. Whereas theory had been the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called three-body parameter determining several properties of the system is universal, even though fundamental assumptions in the theory of the Efimov effect suggest that it should be a variable property that depends on the precise details of the short-range two- and three-body interactions. The present Letter resolves this apparent contradiction by elucidating previously unanticipated implications of the two-body interactions. Our study shows that the three-body parameter universality emerges because a universal effective barrier in the three-body potentials prevents the three particles from simultaneously getting close together. Our results also show limitations on this universality, as it is more likely to occur for neutral atoms but less likely to extend to light nuclei.In recent years extensive theoretical and experimental studies of universal few-body physics have advanced our understanding of universal Efimov physics. Whereas theory had been the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called three-body parameter determining several properties of the system is universal, even though fundamental assumptions in the theory of the Efimov effect suggest that it should be a variable property that depends on the precise details of the short-range two- and three-body interactions. The present Letter resolves this apparent contradiction by elucidating previously unanticipated implications of the two-body interactions. Our study shows that the three-body parameter universality emerges because a universal effective barrier in the three-body potentials prevents the three particles from simultaneously getting close together. Our results also show limitations on this universality, as it is more likely to occur for neutral atoms but less likely to extend to light nuclei.

arXiv:1201.1176Physical Review LettersJun 26, 2012181 citations

{}^{4}\mathrm{He}

atoms. We also extend Efimov's theory to include the effects of deep two-body bound states, which give widths to the Efimov states.