Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1102.3789 · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Efimov physics from a renormalization group perspective

H.‐W. Hammer, Lucas Platter

Published Jun 6, 2011• 29 citations
arXivHTMLPDF

Abstract

We discuss the physics of the Efimov effect from a renormalization group viewpoint using the concept of limit cycles. Furthermore, we discuss recent experiments providing evidence for the Efimov effect in ultracold gases and its relevance for nuclear systems.
DOI
10.1098/rsta.2011.0001

Related papers

Efimov physics in ultracold three-body collisions

Brett D. Esry, José Paulo D'Incao

We discuss some of our recent work on the near-threshold behavior of ultracold three-body collisions and their relation to a recent experiment [T. Kraemer, et al. , Nature 440 , 315 (2006)]. In particular, we discuss the role of Efimov physics in this experiment and other ultracold collisions and how this role can be understood within the adiabatic hyperspherical representation.

Journal of Physics Conference Series•Nov 1, 2007•4 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.

Journal of Physics Conference Series•Oct 1, 2016•0 citations

Onset of a Limit Cycle and Universal Three-Body Parameter in Efimov Physics

Yusuke Horinouchi, Masahito Ueda

The Efimov effect is the only experimentally realized universal phenomenon that exhibits the renormalization-group limit cycle with the three-body parameter parametrizing a family of universality classes. Recent experiments in ultracold atoms have unexpectedly revealed that the three-body parameter itself is universal when measured in units of an effective range. By performing an exact functional renormalization-group analysis with various finite-range interaction potentials, we demonstrate that the onset of the renormalization-group flow into the limit cycle is universal, regardless of short-range details, which connects the missing link between the two universalities of the Efimov physics. A close connection between the topological property of the limit cycle and few-body physics is also suggested.

arXiv:1409.3294•Physical Review Letters•Jan 13, 2015•22 citations

Efimov Physics from the Functional Renormalization Group

Stefan Floerchinger, Sergej Moroz, Richard Schmidt

arXiv:1102.0896•Few-Body Systems•Apr 18, 2011•13 citations

Theoretical Study on Efimov Physics in Ultracold Atoms : 冷却原子気体におけるEfimov状態の物理の理論的研究

晋平 遠藤

•Jan 1, 2017•0 citations

Theoretical study on a renormalization-group limit cycle in Efimov physics

裕理 堀之内

Physics is often said to be universal when microscopically distinct systems show the same lowenergy behavior.In critical phenomena, the universality of the second-order phase transition is elucidated by the renormalization-group (RG) method, which provides a powerful computational tool for the critical exponents of the power-law behavior of observables.In particular, the attraction of different RG-flow trajectories to a small-dimensional sub-theory space accounts for the universal nature.The attraction structure motivates us to extract universal physical observables by investigating the sub-theory space called the renormalized trajectory, onto which RG flows are attracted.To put the motivation forward, we consider the universality in quantum few-body physics, in which the RG exhibits another characteristic flow than the fixed points.The Efimov physics, which is renowned for self-similar trimer states, shows an RG limit-cycle behavior that refers to a periodic RG-flow trajectory.In this thesis, we investigate the relation between the RG limit cycle and the universality in Efimov physics.Firstly, to verify that the RG limit cycle is the renormalized trajectory in Efimov physics, we demonstrate that the RG-flow trajectories of microscopically distinct systems universally exhibit the RG limit-cycle behavior at sufficiently low energy, thereby giving a numerical evidence of the attraction structure of the RG-flow trajectories to the RG limit cycle; in other words, we show that the RG limit cycle behaves as an attractor of various RG flows.To address this point unbiasedly, we perform an exact RG calculation for various effective models of identical bosons that features Efimov physics at low energy.We apply an exact functional renormalization-group (FRG) method to effective separable models for various systems of identical bosons with short-range resonant interactions.For a given microscopic three-body model, we numerically demonstrate for the first time that the RG-flow trajectory converges at the RG limit cycle in the low-energy regime.Physical observables such as Efimov's scaling factor and the three-body parameter can be extracted from the RG limit cycle.Secondly, we investigate the role of RG limit cycle in a four-body extension of Efimov physics, which has attracted considerable attention in recent years.Although the universality in four-body physics has been established both theoretically and experimentally, the relationship between the RG limit cycle and the four-body physics remains an open question.By performing an FRG calculation for a simple effective field theory, we obtain for the first time the RG limit cycle in the four-body sector that reproduces the universality of the four-body physics.As the first attempt, we develop a simple separable pole approximation of the four-body FRG equation and successfully reproduce qualitative features of the four-body physics.A systematic improvement of the approximation quantitatively reproduces the numbers and the binding energies of tetramer states that emerge universally at low energy.2 The restriction r 0 < ∼ R < ∼ a on the length scale limits the binding energy E t of the Efimov trimers as ℏ ma 2 < ∼ E t < ∼ ℏ mr 2 0 .3 A similar discrete scale-invariant phenomenon is known for the doubly excited H -ion, in which two valence electrons are excited from their ground states [16].In the doubly excited H -ion, an interaction between an electron-

•Mar 23, 2017•0 citations
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 is the only experimentally realized universal phenomenon that exhibits the renormalization-group limit cycle with the three-body parameter parametrizing a family of universality classes. Recent experiments in ultracold atoms have unexpectedly revealed that the three-body parameter itself is universal when measured in units of an effective range. By performing an exact functional renormalization-group analysis with various finite-range interaction potentials, we demonstrate that the onset of the renormalization-group flow into the limit cycle is universal, regardless of short-range details, which connects the missing link between the two universalities of the Efimov physics. A close connection between the topological property of the limit cycle and few-body physics is also suggested.
Physics is often said to be universal when microscopically distinct systems show the same lowenergy behavior.In critical phenomena, the universality of the second-order phase transition is elucidated by the renormalization-group (RG) method, which provides a powerful computational tool for the critical exponents of the power-law behavior of observables.In particular, the attraction of different RG-flow trajectories to a small-dimensional sub-theory space accounts for the universal nature.The attraction structure motivates us to extract universal physical observables by investigating the sub-theory space called the renormalized trajectory, onto which RG flows are attracted.To put the motivation forward, we consider the universality in quantum few-body physics, in which the RG exhibits another characteristic flow than the fixed points.The Efimov physics, which is renowned for self-similar trimer states, shows an RG limit-cycle behavior that refers to a periodic RG-flow trajectory.In this thesis, we investigate the relation between the RG limit cycle and the universality in Efimov physics.Firstly, to verify that the RG limit cycle is the renormalized trajectory in Efimov physics, we demonstrate that the RG-flow trajectories of microscopically distinct systems universally exhibit the RG limit-cycle behavior at sufficiently low energy, thereby giving a numerical evidence of the attraction structure of the RG-flow trajectories to the RG limit cycle; in other words, we show that the RG limit cycle behaves as an attractor of various RG flows.To address this point unbiasedly, we perform an exact RG calculation for various effective models of identical bosons that features Efimov physics at low energy.We apply an exact functional renormalization-group (FRG) method to effective separable models for various systems of identical bosons with short-range resonant interactions.For a given microscopic three-body model, we numerically demonstrate for the first time that the RG-flow trajectory converges at the RG limit cycle in the low-energy regime.Physical observables such as Efimov's scaling factor and the three-body parameter can be extracted from the RG limit cycle.Secondly, we investigate the role of RG limit cycle in a four-body extension of Efimov physics, which has attracted considerable attention in recent years.Although the universality in four-body physics has been established both theoretically and experimentally, the relationship between the RG limit cycle and the four-body physics remains an open question.By performing an FRG calculation for a simple effective field theory, we obtain for the first time the RG limit cycle in the four-body sector that reproduces the universality of the four-body physics.As the first attempt, we develop a simple separable pole approximation of the four-body FRG equation and successfully reproduce qualitative features of the four-body physics.A systematic improvement of the approximation quantitatively reproduces the numbers and the binding energies of tetramer states that emerge universally at low energy.2 The restriction r 0 < ∼ R < ∼ a on the length scale limits the binding energy E t of the Efimov trimers as ℏ ma 2 < ∼ E t < ∼ ℏ mr 2 0 .3 A similar discrete scale-invariant phenomenon is known for the doubly excited H -ion, in which two valence electrons are excited from their ground states [16].In the doubly excited H -ion, an interaction between an electron-