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Resonantly Interacting Fermions In a Box
Quantum Gases · Submitted 9 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: \xi_S <= 0.383(1).
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The abstract, sentence by sentence
We use two fundamental theoretical frameworks to study the finite-size (shell) properties of the unitary gas in a periodic box: 1) an ab initio Quantum Monte Carlo (QMC) calculation for boxes containing 4 to 130 particles provides a precise and complete characterization of the finite-size behavior, and 2) a new Density Functional Theory (DFT) fully encapsulates these effects. The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: \xi_S <= 0.383(1). We also apply the new functional to few-particle harmonically trapped systems, comparing with previous calculations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We use two fundamental theoretical frameworks to study the finite-size (shell) properties of the unitary gas in a periodic box: 1) an ab initio Quantum Monte Carlo (QMC) calculation for boxes containing 4 to 130 particles provides a precise and complete characterization of the finite-size behavior, and 2) a new Density Functional Theory (DFT) fully encapsulates these effects. | method 0.68 | 0.95 | 0.12 | asserted 1.00 |
| s1 | The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: \xi_S <= 0.383(1). | result 1.00 | 0.92 | 0.76 | asserted 1.00 |
| s2 | We also apply the new functional to few-particle harmonically trapped systems, comparing with previous calculations. | contribution 0.92 | 0.92 | 0.03 | asserted 0.89 |
What was examined, and what was not
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The paper
Original abstract
We use two fundamental theoretical frameworks to study the finite-size (shell) properties of the unitary gas in a periodic box: 1) an ab initio Quantum Monte Carlo (QMC) calculation for boxes containing 4 to 130 particles provides a precise and complete characterization of the finite-size behavior, and 2) a new Density Functional Theory (DFT) fully encapsulates these effects. The DFT predicts vanishing shell structure for systems comprising more than 50 particles, and allows us to extrapolate the QMC results to the thermodynamic limit, providing the tightest bound to date on the ground-state energy of the unitary gas: \xi_S <= 0.383(1). We also apply the new functional to few-particle harmonically trapped systems, comparing with previous calculations.
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References
How the literature uses it
11 arXiv papers cite this in 30 sentences
Papers citing it · 19 sentences without a confident label
Uses its data or values 3 papers
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A more recent fixed-node calculation sets an upper bound for $ξ_N,N$ at $0.383(1)$ for $N$ between $2$ and $65$ [ref] .
Precision benchmark calculations for four particles at unitarity · Results for $ξ$ and the need for precision benchmarks · 0.89
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where $g_DD ≈0.6 a_ff$ is the dimer-dimer scattering length [ref] , and $ξ= 0.3742(5)$ [ref] is the universal Bertsch parameter [ref] , combining experiment [ref] and QMC [ref] values.
Detecting Entrainment in Fermi-Bose Mixtures · Theory · 0.98
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The Bertsch parameter $ξ≃0.38$ [ref] governs the relationship between the chemical potential and the Fermi energy.
Bulk viscosity and conformal symmetry breaking in the dilute Fermi gas near unitarity · Outlook · 1.00
Compares with it 3 papers
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As before [ref] , the best fit gap parameter $η$ and inverse effective mass $α$ are inconsistent with the values $η= 0.50(5)$ and $α= 1.09(2)$ obtained from the $N_+=66$ QMC quasiparticle dispersion relation [ref] , and the values $η= 0.45(5)$ [ref] and $η= 0.44(3)$ [ref] extracted from experimental data.
Effective-Range Dependence of Resonantly Interacting Fermions · Box · 0.91
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This is consistent with the range dependence found in Ref. [ref] .
Precision benchmark calculations for four particles at unitarity · Summary and discussion · 0.88
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Some influence could come also due to the differences between the extrapolation methods employed in this work and in Ref. [ref] .
Atomic Fermi gas at the unitary limit by quantum Monte Carlo methods: Effects of the interaction range · Conclusions · 0.97
Cites it as background 2 papers
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It is a local functional of the density $ρ$ and two additional densities: a kinetic density $τ(x) ∝⟨∇ψ^†·∇ψ|$⟩ (following the Kohn-Sham formulation [ref] ) which is required to model finite-size (shell) effects, and an anomalous density$ν∝⟨ψψ|$⟩ required to model pairing effects (see [ref] for a discussion).
Validating Simple Dynamical Simulations of the Unitary Fermi Gas · The SLDA · 0.90
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The question of how the unitary gas approaches the thermodynamic limit has also been studied in [ref] .
Effective-Range Dependence of Resonantly Interacting Fermions · Introduction · 0.90
Discussion
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