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Universal corrections to the superfluid gap in a cold Fermi gas
Nuclear Theory · Submitted 29 Jul 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Together, these effects are found to reduce the gap at low densities.
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The abstract, sentence by sentence
A framework for computing the superfluid gap in an effective field theory (EFT) of fermions interacting via momentum-independent contact forces is developed. The leading universal corrections in the EFT are one-loop in-medium effects at the Fermi surface, and reproduce the well-known Gor'kov-Melik-Barkhudarov result. The complete subleading universal corrections are presented here, and include one-loop effects away from the Fermi surface, two-loop in-medium effects, as well as modifications to the fermion propagator. Together, these effects are found to reduce the gap at low densities. Applications to neutron superfluidity in neutron stars are also discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A framework for computing the superfluid gap in an effective field theory (EFT) of fermions interacting via momentum-independent contact forces is developed. | contribution 0.70 | 0.88 | 0.05 | asserted 1.00 |
| s1 | The leading universal corrections in the EFT are one-loop in-medium effects at the Fermi surface, and reproduce the well-known Gor'kov-Melik-Barkhudarov result. | result 0.62 | 0.28 | 0.10 | asserted 1.00 |
| s2 | The complete subleading universal corrections are presented here, and include one-loop effects away from the Fermi surface, two-loop in-medium effects, as well as modifications to the fermion propagator. | contribution 0.99 | 0.92 | 0.13 | asserted 1.00 |
| s3 | Together, these effects are found to reduce the gap at low densities. | result 1.00 | 0.94 | 0.66 | asserted 1.00 |
| s4 | Applications to neutron superfluidity in neutron stars are also discussed. | contribution 0.88 | 0.62 | 0.04 | asserted 0.74 |
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The paper
Original abstract
A framework for computing the superfluid gap in an effective field theory (EFT) of fermions interacting via momentum-independent contact forces is developed. The leading universal corrections in the EFT are one-loop in-medium effects at the Fermi surface, and reproduce the well-known Gor'kov-Melik-Barkhudarov result. The complete subleading universal corrections are presented here, and include one-loop effects away from the Fermi surface, two-loop in-medium effects, as well as modifications to the fermion propagator. Together, these effects are found to reduce the gap at low densities. Applications to neutron superfluidity in neutron stars are also discussed.
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References
How the literature uses it
1 arXiv paper cite this in 3 sentences
What it cites · 21 sentences without a confident label
Uses the method or tool of 17 papers
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This technique is based on deriving the three-dimensional representation of a Feynman diagram by integrating the energy components of loop integrals analytically [ref] , performing the singularity analysis and regularization in the integration space of the remaining spatial components [ref] , and finally numerically performing the regularized integral by direct Monte-Carlo integration (see [ref] for a comprehensive review of the method and [ref] for recent applications).
From loops to trees by-passing Feynman's theorem · Details of the NNLO Calculation · 1.00
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This technique is based on deriving the three-dimensional representation of a Feynman diagram by integrating the energy components of loop integrals analytically [ref] , performing the singularity analysis and regularization in the integration space of the remaining spatial components [ref] , and finally numerically performing the regularized integral by direct Monte-Carlo integration (see [ref] for a comprehensive review of the method and [ref] for recent applications).
A Tree-Loop Duality Relation at Two Loops and Beyond · Details of the NNLO Calculation · 1.00
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This technique is based on deriving the three-dimensional representation of a Feynman diagram by integrating the energy components of loop integrals analytically [ref] , performing the singularity analysis and regularization in the integration space of the remaining spatial components [ref] , and finally numerically performing the regularized integral by direct Monte-Carlo integration (see [ref] for a comprehensive review of the method and [ref] for recent applications).
Causality and loop-tree duality at higher loops · Details of the NNLO Calculation · 1.00
Uses data or values from 1 paper
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In neutron-neutron scattering, the scattering length is $a^-1≈-10.7 MeV$ [ref] , and perturbation theory is expected to break down around $k_F ≈17 MeV$.
The Low-Energy Neutron-Proton Scattering Parameters and the Deuteron · The Gap at NNLO · 0.96
Compares with 2 papers
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As $a <0$ (attractive potential), the gap is reduced relative to $Δ_GM$, in agreement with the QMC simulations in Ref. [ref] .
Strongly paired fermions: Cold atoms and neutron matter · Introduction · 0.82
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It is noteworthy that recent work [ref] , which incorporates effects beyond the GM approximation, and extends from weak coupling through the BCS/BEC crossover region, is also in good agreement with the QMC result at $k_F a = -1$.
Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs · The Gap at NNLO · 0.91
Cites as background 15 papers
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In parallel, there have also been ab initio approaches that determine the gap using Quantum Monte Carlo (QMC) simulations [ref] .
Low-density neutron matter · Introduction · 0.82
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In parallel, there have also been ab initio approaches that determine the gap using Quantum Monte Carlo (QMC) simulations [ref] .
Quantum Monte Carlo approaches to nuclear and atomic physics · Introduction · 0.82
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In parallel, there have also been ab initio approaches that determine the gap using Quantum Monte Carlo (QMC) simulations [ref] .
Equation of state of superfluid neutron matter and the calculation of $^1S_0$ pairing gap · Introduction · 0.82
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