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The Unitary Fermi Gas in a Harmonic Trap and its Static Response
Quantum Gases · Submitted 16 Nov 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find the leading order correction to be negative, and predict the q^2 coefficient of the long-range static response c = 1.5(3) - a factor of two smaller than predicted by mean-field theory - thereby establishing a new and experimentally measurably universal constant.
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The abstract, sentence by sentence
We use harmonically trapped systems to find the leading gradient corrections of the supefluid local density approximation (SLDA) - a density functional theory (DFT) describing the unitary Fermi gas (UFG). We find the leading order correction to be negative, and predict the q^2 coefficient of the long-range static response c = 1.5(3) - a factor of two smaller than predicted by mean-field theory - thereby establishing a new and experimentally measurably universal constant.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We use harmonically trapped systems to find the leading gradient corrections of the supefluid local density approximation (SLDA) - a density functional theory (DFT) describing the unitary Fermi gas (UFG). | method 0.57 | 0.93 | 0.07 | asserted 0.99 |
| s1 | We find the leading order correction to be negative, and predict the q^2 coefficient of the long-range static response c = 1.5(3) - a factor of two smaller than predicted by mean-field theory - thereby establishing a new and experimentally measurably universal constant. | result 1.00 | 0.95 | 0.88 | asserted 1.00 |
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The paper
Original abstract
We use harmonically trapped systems to find the leading gradient corrections of the supefluid local density approximation (SLDA) - a density functional theory (DFT) describing the unitary Fermi gas (UFG). We find the leading order correction to be negative, and predict the q^2 coefficient of the long-range static response c = 1.5(3) - a factor of two smaller than predicted by mean-field theory - thereby establishing a new and experimentally measurably universal constant.
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References
How the literature uses it
7 arXiv papers cite this in 17 sentences
Papers citing it · 11 sentences without a confident label
Uses its data or values 2 papers
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The magnitude of the gradient corrections is relatively small $λ≈- 0.1$ (and somewhat surprisingly negative) [ref] and the effective mass is close to the bare mass value, as $α≈1.1$ [ref] .
Time-Dependent Density Functional Theory and the Real-Time Dynamics of Fermi Superfluids · Unitary Fermi Gas · 0.88
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The value for $≈1.5(3)$ follows from an analysis of gradient corrections to harmonically trapped gases [ref] .
Validating Simple Dynamical Simulations of the Unitary Fermi Gas · Linear Response · 0.87
Compares with it 1 paper
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There are also numerical studies [ref] , though these deal with the opposite regime of small charge, where the quantized nature of the problem is apparent, and it is not clear how to make a direct comparison between our respective results.
The large-charge expansion in nonrelativistic conformal field theories · Summary of the results and comparison with the literature · 0.98
Cites it as support 1 paper
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The absence of a Weizsäcker term gives the expected analytic behavior of the condensate at the vortex core [ref] and better describes the dynamics of colliding superfluids [ref] .
Validating Simple Dynamical Simulations of the Unitary Fermi Gas · The ETF Model · 0.97
Cites it as background 1 paper
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For $T→0$ the corrections to LDA have been previously studied in Refs. [ref] .
The Shear Viscosity in an Anisotropic Unitary Fermi Gas · Discussion on $κ_LDA$ · 0.91
What it cites · 47 sentences without a confident label
Uses data or values from 2 papers
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Finally, we include the latest experimental results as a (yellow) band [ref] and the best fit value of $ξ= 0.3742(5)$ to all homogeneous ab initio QMC results from [ref] at $x=0$.
Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas · Introduction · 0.85
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Finally, we include the latest experimental results as a (yellow) band [ref] and the best fit value of $ξ= 0.3742(5)$ to all homogeneous ab initio QMC results from [ref] at $x=0$.
Effective-Range Dependence of Resonantly Interacting Fermions · Introduction · 0.85
Cites as support 1 paper
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Superfluid hydrodynamic phenomenology [ref] and vortex dynamics (appendix [ref]) suggest that $= 0$.
Shock waves in strongly interacting Fermi gas from time-dependent density functional calculations · Introduction · 0.96
Cites as background 10 papers
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At low-energies, the UFG can be characterized by a superfluid EFT describing phonon dynamics [ref] .
General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas · Introduction · 0.81
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The SLDA was originally constrained by QMC calculations of the continuum state, and validated with QMC calculations in a harmonic trap [ref] .
Universal properties of a trapped two-component Fermi gas at unitarity · Introduction · 0.81
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The SLDA was originally constrained by QMC calculations of the continuum state, and validated with QMC calculations in a harmonic trap [ref] .
Unitary Fermi Gas in a Harmonic Trap · Introduction · 0.81
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