Pith. Sign in

REVIEW

Universality in Few-body Systems with Large Scattering Length

PaperPDF from arXiv

data files

ReviewThe objections and verdict, as JSON Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Eric Braaten (Ohio State U.), H.-W. Hammer (INT, Bonn U.)

Other Condensed Matter · Submitted 16 Oct 2004 · 237 references

Pith's verdict: The standard reference on Efimov physics: careful, well-attributed, and honest about what is input rather than derived — cite it, but check Eq. (205) against the published version first.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

  1. T0 AI review An AI read the paper and answered a fixed list of questions.
  2. T1 Audit Automatic checks that the references and files the paper relies on exist and match.
  3. T2 Compute The paper's code or calculations re-run with the same results.
  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 6 minor · Ask about this paper · The compiled record · Read the full review →
Challenge this review Comment (0) Read on arXiv ↗
Cite ▾
arXiv IDcond-mat/0410417 (version 3)
Pith IDMAXSICFT, Pith's permanent record of this paper and its review
CitationBonn U.), Eric Braaten (Ohio State U.), H.-W. Hammer (INT. "Universality in Few-body Systems with Large Scattering Length." arXiv:cond-mat/0410417 (2004). https://pith.science/paper/MAXSICFT
Cite this reviewBibTeX for Pith's review of this paper
Claim paper

Why Pith says this

Highlight any text to comment on it.

Referee report

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The paper argues that three identical bosons with a large scattering length have a universal low-energy spectrum and scattering matrix fixed by the scattering length and a single three-body parameter, with a geometric Efimov ladder in the共振

The reading

The paper is a review arguing that when short-range interactions are tuned so the two-body scattering length $a$ is much larger than the interaction range, the low-energy behavior of three identical bosons becomes universal: it is fixed by $a$ and by one additional three-body parameter $§kappa_*$, not by the shape of the potential. In the resonant limit $a§to§pm§infty$, the three-body bound states form a geometric sequence with adjacent binding energies in the ratio $e^{-2§pi/s_0}§approx 1/515.03$, where $s_0§approx1.00624$ solves a transcendental equation. Scattering observables then depend on $a$ and energy through log-periodic functions, so rescaling $a$ by $e^{§pi/s_0}§approx22.7$ maps the physics back onto itself. The review presents the hyperspherical formalism, Efimov's radial law, and effective field theory as three routes to the same constraints, and it collects the universal numbers needed for atom-dimer scattering, three-body recombination, and three-atom scattering. A reader should care because this would turn a complicated short-range quantum problem into a small set of universal curves that can be compared across atoms, nuclei, and other few-body systems.

What carries the argument

The load-bearing device is Efimov's radial law, implemented through hyperspherical coordinates. The three-body wave function is decomposed into hyperradial and hyperangular parts; in the scale-invariant region $§ell§ll R§ll |a|$ the hyperradial equation reduces to a $1/R^2$ problem with imaginary index $s_0$, so the wave function oscillates logarithmically in $R$. Matching at short distances fixes the phase $§theta_*=-s_0§ln(cH/§Lambda_0)$, and matching through the long-distance region gives a unitary matrix $s_{ij}$ that depends only on the angular variable $§xi$. The $S$-matrix is then assembled from these pieces, with bound states appearing as poles when $e^{2i§theta_*}s_{11}=1$. This is what converts an apparently potential-dependent three-body calculation into a universal, log-periodic dependence on $a§kappa_*$.

Extended reading notes

Core claim

The central claim is that three identical bosons with a large scattering length have a universal low-energy sector in which the only inputs are $a$ and a three-body parameter $§kappa_*$; all dependence on short-distance physics is absorbed into $§kappa_*$ and universal functions of one angular variable. In the resonant limit the spectrum is asymptotically geometric, $E_T^{(n+1)}/E_T^{(n)}§to e^{-2§pi/s_0}§approx1/515.03$, and the continuous scaling symmetry of the two-body problem is reduced to a discrete scaling symmetry with factor $e^{§pi/s_0}§approx22.7$. The review's derivation combines a hyperspherical reduction to a one-dimensional hyperradial problem, a short-distance matching condition that introduces the scaling-violation parameter, and Efimov's radial law, which expresses the full three-body $S$-matrix in terms of a few universal functions and the angle $§theta_*$ containing $§ln(a§kappa_*)$. The result is not merely that Efimov states exist; it is that their positions and the associated scattering observables are tied together by log-periodic formulas, so measuring one three-body quantity can fix the rest.

Load-bearing premise

The clean single-parameter structure of Section 6 assumes that probability reaching short distances is totally reflected, i.e. $|A|=|B|$ for the incoming and outgoing hyperradial waves, which holds only if there are no deep two-body bound states into which the probability can drain.

Editorial extensions

If this is right

  • Once $a$ and $§kappa_*$ are fixed, atom-dimer scattering lengths and effective ranges follow log-periodic universal curves, so one measurement can predict others.
  • The Efimov spectrum is not a set of evenly spaced energies; adjacent trimers differ by about 515 near resonance, but the ratio can range far from 515 away from resonance.
  • Three-body recombination and three-atom scattering can be calculated from the same universal functions, giving a common language for ultracold atoms and nuclear few-body systems.
  • The discrete scaling symmetry is the observable signature of a renormalization-group limit cycle, so the three-body problem supplies a physical example of a limit cycle rather than a fixed point.
  • Deviations from universality can be organized systematically: effective-range corrections enter as powers of $§ell/a$, while deep bound states require the extended treatment of Section 7.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the universal curves hold across atomic species, a single well-chosen three-body measurement could calibrate $§kappa_*$ for a whole isotope and turn three-body loss into a practical probe of short-distance physics.
  • The same log-periodic structure should constrain four-body and larger clusters only if their own short-distance matching preserves the limit-cycle symmetry; otherwise the clean three-body universality may not extend naively.
  • The review's emphasis on one three-body parameter suggests that systems with deep two-body bound states are best treated as a different universality class, not as small perturbations, because the reflection condition fails qualitatively.
  • A useful cross-check would be to extract $§kappa_*$ independently from trimer binding energies and from atom-dimer scattering; agreement would test the radial-law assembly, while disagreement would point to a missing short-distance channel.
Original 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.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,731 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.05 0.30 asserted 1.00
s1 In the 2-body sector, the universal properties are familiar and depend only on the scattering length a. background 1.00 0.05 0.05 asserted 1.00
s2 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. background 0.98 0.06 0.11 asserted 1.00
s3 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. background 0.85 0.09 0.14 asserted 1.00
s4 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. contribution 1.00 0.72 0.11 asserted 0.98
s5 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. method 1.00 0.46 0.04 asserted 0.99
s6 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. contribution 0.87 0.44 0.09 asserted 0.87

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.96.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. Attractive square well potential with range
Figure 2. Two-body observables for the attractive square-wel
Figure 3. Probability distribution for the scattering length
Figure 4. Van der Waals potential with a hard-core radius
Figure 5. The critical values can be reached by fine-tuning eith
Figure 6. Probability distribution for the scattering length
Figure 7. Mechanisms for generating a large scattering length
Figure 8. The scattering length a as a function of the magnetic field B near a Feshbach resonance with abg < 0 and cres > 0. Feshbach resonances in alkali atoms can be created by tuning the magnetic field [27,28]. In this case, the open channel consists of a pair of atoms in a specific hyperfine state |f, mf i. The closed channel consists of a pair of atoms in different hyperfine states with a higher scattering threshold. The weak cou￾pling between the channels is provided by the hyperfine interaction. Since different hyperfine states have different magnetic moments, a magnetic field can be…
Figure 9. (a) A square well potential with a single shallow boun
Figure 10. The pressure P versus the temperature T for a liquid-gas system with a critical point at (Tc,Pc). ior. An example is the behavior of the coexistence curves ρliq(T) and ρgas(T) near the critical point. At T = Tc, they are both equal to the critical density ρc. As T → Tc from below, the deviations of ρliq(T) and ρgas(T) from ρc have a power-law behavior: ρliq(T) − ρc −→+A(Tc − T) β , (44a) ρgas(T) − ρc −→ −A(Tc − T) β . (44b) The coefficient A varies widely from substance to substance, but the critical exponent β is a universal number. It has the same value β = 0.325 for all liquid–…
Figure 11. The magnetic field B versus the temperature T for a ferromagnetic material with one easy axis of magnetization and a critical point at (Tc,B = 0). Another familiar example of a system in which critical phenomena can occur is a ferromagnetic material with one easy axis of magnetization. The ther￾35
Figure 12. Nesting Russian dolls with a discrete scaling facto
Figure 13. Energy spectrum for the continuum limit of the Glaze
Figure 14. The behavior of g(Λ)/h as a function of Λ/Λ0 for the case g(Λ0)/h = 1 and λ0 = 2. the accumulation point is approached, the ratio of adjacent negative energy levels approaches λ0. The spectrum is characterized by an asymptotic discrete scaling symmetry with discrete scaling factor λ0. In the continuum limit, g becomes a function of the ultraviolet cutoff Λ, and the discrete RG transfor￾mation in Eq. (54) becomes a continuous RG flow: arctan g(Λ) h = arctan g(Λ0) h − π ln λ0 ln Λ Λ0 . (56) The coupling constant g(Λ) is a periodic function of ln(Λ). Thus the renor￾malization of g(Λ)…
Figure 15. Differential cross section for atom-atom scatterin
Figure 16. Normalized probability distribution dP/dr for the separation r of the atoms in the shallow dimer as a function of r/a. The wave function of the dimer at separations r ≫ ℓ is also universal. The unnormalized coordinate-space wave function is ψD(r) = 1 r e −r/a , (63) where r = |r| is the separation of the two atoms. The normalized probability distribution for the separation r of the atoms in the shallow dimer is shown in
Figure 17. The a −1–K plane for the 2-body problem. The allowed region for atom-atom scattering states are the two quadrants labelled AA. The heavy line labelled D is the shallow dimer. The cross-hatching indicates the 2-atom threshold. The a −1–K plane for the 2-body system in the scaling limit is shown in
Figure 18. One of the three possible sets of Jacobi coordinates
Figure 19. Three-body configurations with the same hyperradiu
Figure 20. The three lowest channel eigenvalues λn(R) for a > 0 (solid lines) and for a < 0 (dashed lines). The physical channel eigenvalues λn(R) can be obtained by solving Eq. (129) numerically. The lowest three eigenvalues for a > 0 and the lowest three eigenvalues for a < 0 are shown as functions of R/|a| in
Figure 21. The three lowest hyperspherical potentials
Figure 22. The normalized probability distributions
Figure 23. The a −1–K plane for the 3-body problem. The allowed regions for 3-atom scattering states and atom-dimer scattering states are labelled AAA and AD, re￾spectively. The heavy lines labeled T are three of the infinitely many branches of Efimov states. The cross-hatching indicates the threshold for scattering states. The axes labelled 1/a and K are actually H1/4 cos ξ and H1/4 sin ξ. The a −1–K plane for three identical bosons in the scaling limit is shown in
Figure 24. The energy variable K for the branch of Efimov trimers labelled by n = n∗ as a function of 1/a. In the resonant limit, the binding wave number is κ∗. The branch disappears through the atom-dimer threshold at a = a∗ and through the 3-atom threshold at a = a ′ ∗ . Changing 1/a continuously from a large positive value to a large negative value corresponds to the vertical dashed line in
Figure 25. The universal function ∆(ξ) for −π < ξ < −1 4 π. There have been many calculations of the binding energies of the Efimov states by solving the Schr¨odinger equation for various 2-body potentials. In principle, the function ∆(ξ) could be mapped out by carrying out such calculations for many different sequences of potentials that are approaching the scaling limit. The function ∆(ξ) can be calculated more directly using the renormalized zero-range model [44] or using effective field theory [61,62], because these methods allow the range to be set to zero so that one can carry out…
Figure 26. Comparison of the analytic approximations in Eqs. (
Figure 27. The atom-dimer scattering length aAD (solid line) and the effective range rs,AD (dashed line) as functions of aΛ∗. The vertical dotted lines indicate the loca￾tion of the poles in aAD. this points, but rs,ADa 2 AD behaves smoothly. The atom-dimer effective range achieves its minimum value at the points a = (e π/s0 ) n0.94/Λ∗. Its value at the minimum is consistent with zero to within the numerical accuracy. If it really is zero, it would indicate that the coefficient of a in Eq. (218) is the square of an expression that is linear in tan[s0 ln(aΛ∗) + 1.07]. This would require an add
Figure 28. The S-wave contribution to the differential cross se
Figure 29. The 3-body recombination rate constant αshallow in units of ¯ha4/m as a function of aΛ∗. We denote the contribution to the rate constant α from 3-body recombination into the shallow dimer by αshallow. By dimensional analysis, it is proportional to ¯ha4/m with a coefficient that depends only on aκ∗. Petrov has derived a remarkable analytic expression for αshallow [96]: αshallow = 128π 2 (4π − 3 √ 3) sinh2 (πs0) + cosh2 (πs0) tan2 [s0 ln(aκ∗) + γ] ha¯ 4 m , (228) where γ is a real numerical constant. The maximum value of the coefficient of ha¯ 4/m is Cmax = 128π 2 (4π
Figure 30. Universal scaling curves for E (N−1) T ma2/¯h 2 vs. E (N) T ma2/¯h 2 for (a) a > 0 and (b) a < 0. E (N) T and E (N−1) T are the binding energies of the shallowest and second shallowest Efimov states. aD = (mED/h¯ 2 ) 1/2 . Thus ln Λ∗ ranges over 10% of its complete period of π/s0, which is enough to trace out a significant fraction of the universal scal￾ing curve. In
Figure 31. The universal scaling curve in Fig. 30(a) in the regi
Figure 32. Universal scaling curve for aAD/a vs. E (N) T /ED, where E (N) T is the binding energy of the shallowest Efimov state. The universal scaling curve for the scaling variables E (1) T /ED and aAD/a was calculated in Ref. [90] using the effective field theory of Ref. [61,62] and is shown in
Figure 33. The S-wave contribution to the differential cross se
Figure 34. The 3-body recombination rate constants αshallow (with large-amplitude oscillations) and αdeep (with small-amplitude oscillations) in units of ¯ha4/m as functions of aΛ∗ for a > 0 and different values of η∗. If there are deep molecules, the radial law for the S-matrix element for 3- body recombination into the shallow dimer is given in Eq. (249b). For energies E = ¯h 2 κ 2/m just above the dimer-breakup threshold, the entries of the matrix sij have the expansions given in Eqs. (233). The limiting behavior of the S￾matrix element as E → 0 + is obtained by substituting θ∗ → θ∗ + iη∗ i
Figure 35. The 3-body recombination rate constant αdeep in units of ¯ha4/m as a function of |a|Λ∗ for a < 0 and different values of η∗. We now consider the consequences of the radial law in Eq. (254b) for 3-body recombination into deep molecules in the case of negative scattering length a < 0. As the energy E = ¯h 2K2/m approaches the 3-atom threshold E = 0, the limiting behavior of the entries of the matrix s are given in (242). Thus the limiting behavior of the sum of the squares of the S-matrix elements in Eq. (254b) is X X |SX,AAA| 2 −→2d0aK sinh(2η∗) sin2 (θ∗ + γ) + sinh2 η∗ , as E
Figure 36. The dimer relaxation rate constant β in units of ¯ha/m for different values of η∗ as a function of aΛ∗. The total energy of the atom and dimer is expressed in terms of the common wave number k of the atom and dimer in Eq. (206). Just above the atom-dimer threshold, the nonzero entries of the unitary matrix s have the form given in Eq. (214). The resulting expression for the sum of the squares of the S-matrix elements in Eq. (254a) reduces to X X |SX,AD| 2 −→ 2b0ak sinh(2η∗) sin2 (θ∗ + β ′ ) + sinh2 η∗ , as E → −ED . (274) The constants b0 and β ′ are calculated in Ref. [130]. The…
Figure 37. The binding wave numbers κ for the deepest bound states as a function of ln(r0κ∗) for s0 = 2 and the delta-shell regularization potential. We now consider the bound-state spectrum. In the effective potential, the equation for the binding wave number κ defined by E = −h¯ 2 κ 2/2m is 133
Figure 38. The coupling constant λ(r0) for the delta-shell regularization potential as a function of ln(r0κ∗) for s0 = 2. We can interpret r0 as a short-distance cutoff and ¯h 2 /mr2 0 as the corresponding ultraviolet energy cutoff. The tuning of λ(r0) can be interpreted as the renor￾malization of the coupling constant. As shown in
Figure 39. Feynman rules for the Lagrangian in Eq. (293): (a) th
Figure 40. Diagrammatic equations for the 2 → 2 off-shell amplitude: (a) the pertur￾bative expansion in g2, and (b) the integral equation. invariant under the permutation of n internal lines. For example, the second diagram in
Figure 41. The dimensionless 2-body coupling constant ˆg
Figure 42. Feynman rule for the 3-body contact interaction.
Figure 43. Feynman diagrams for the 3 ( ) → 3 elastic scattering amplitude: (a) a tree +  diagram that contributes to the E−1 term, (b) one-loop diagrams that contribute to the E−1/2 term, (c) two-loop diagrams that contribute to the ln(E) term. elastic scattering. At the leading order g 3 2 , the E−1/2 term comes from the 1-particle-irreducible 1-loop diagram in
Figure 44. Simple integral equation for the truncated connect
Figure 45. Feynman rules for the Lagrangian in Eq. (324): (a) th
Figure 46. Feynman rules for the Lagrangian in Eq. (324): inter
Figure 47. Diagrammatic equations for the complete diatom pro
Figure 48. The integral equation for the 3-body amplitude
Figure 49. Amplitudes for (a) atom-dimer scattering, (b) 3-bo
Figure 50. The dimensionless 3-body coupling constant ˆg
Figure 51. Feynman diagrams with a single insertion of the
Figure 52. Discrete scaling factor e π/s0 for two particles of equal mass m1 = m2 as a function of the mass ratio m1/m3 for the case in which all three pairs have large scattering lengths. The particles 1 and 2 can be either identical bosons or distinguishable. The dot indicates the case of three identical bosons. We first consider the case in which all three pairs have a large scattering length. This excludes the possibility of any pair of particles being identical fermions. The Efimov effect occurs if the lowest channel eigenvalue λ0(R) in the scaling limit has a negative value at R = 0.…
Figure 53. In the case of two heavy atoms and a third atom that is much lighter, the Efimov effect can be understood intuitively using the Born-Oppenheimer ap￾proximation [162]. We take the heavy masses to be m1 = m2 = M and the light mass to be m3 = m with m ≪ M. The hyperradius R defined in Eq. (384) can be identified with the separation r12 of the two heavy atoms. We take the co￾ordinates of the three particles in the center-of-mass frame to be r1 = +1 2R, r2 = − 1 2R, and r3 = r. We assume that the potential between the heavy atoms can be neglected, so that the 3-body potential V (r1, r2,…
Figure 54. The Phillips line at leading order (dash-dotted lin
Figure 55. Borromean rings. The separation of scales in halo nuclei leads to universal properties that are 190
Figure 56. Universal scaling curves for the binding energies o
Figure 57. The correlation between the binding energies of the
Figure 58. Leading order range corrections. Not shown are diag

Figures reproduced from arXiv:cond-mat/0410417 by the authors.

References
How later papers used it

258 later papers cite it

Evidence: substantial. 218 of the citing papers share no author with it, and 27 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 520 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 3 of 12 papers with this label
Uses its data or values 4 of 7 papers with this label · 2 by the same authors

By the same authors

Compares with it 4 of 14 papers with this label · 1 by the same authors

By the same authors

How the literature uses it

120 arXiv papers cite this in 218 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 125 sentences without a confident label

Builds on it 1 paper
Uses its method or tool 6 papers
Uses its data or values 4 papers
Compares with it 5 papers
Cites it as support 3 papers
  • Indeed, the “Russian doll superconductivity model” of Leclair et al. [ref] provides a single flowing coupling $u$ that illustrates what we have in mind.

    RG flows, cycles, and c-theorem folklore · Introduction · 0.97

  • This decoupling suggests that observables such as the decay width might be dictated by universal geometric constraints rather than by detailed internal structure [ref] .

    Universal Properties of Near-Threshold Single-Neutron Resonances · Introduction · 0.96

  • As pointed out in Refs. [ref] , the appearance of Efimov states requires an oscillatory three-body force, which explicitly breaks the approximate conformal symmetry that could otherwise give rise to unparticle behavior.].

    Short-range production of three bottom mesons · Introduction · 0.98

Cites it as background 58 papers

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.