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Validating Simple Dynamical Simulations of the Unitary Fermi Gas
Quantum Gases · Submitted 20 Aug 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For non-linear dynamics such as vortex generation, the ETF provides a semi-quantitative description of SLDA dynamics as long as the fluctuations do not have significant power near the pair breaking threshold, otherwise the dynamics of the ETF cannot be trusted.
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The abstract, sentence by sentence
We present a comparison between simulated dynamics of the unitary fermion gas using the superfluid local density approximation (SLDA) and a simplified bosonic model, the extended Thomas Fermi (ETF) with a unitary equation of state. Small amplitude fluctuations have similar dynamics in both theories for frequencies far below the pair breaking threshold and wave vectors much smaller than the Fermi momentum, and the low frequency linear responses match well for surprisingly large wave vectors, even up to the Fermi momentum. For non-linear dynamics such as vortex generation, the ETF provides a semi-quantitative description of SLDA dynamics as long as the fluctuations do not have significant power near the pair breaking threshold, otherwise the dynamics of the ETF cannot be trusted. Nonlinearities in the ETF tends to generate high-frequency fluctuations, and with no normal component to remove this energy from the superfluid, features like vortex lattices cannot relax and crystallize as they do in the SLDA. We present a heuristic diagnostic for validating the reliability of ETF dynamics by considering the approximate conservation of square of the gap: $\int|\Delta|^2$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a comparison between simulated dynamics of the unitary fermion gas using the superfluid local density approximation (SLDA) and a simplified bosonic model, the extended Thomas Fermi (ETF) with a unitary equation of state. | contribution 0.97 | 0.92 | 0.07 | asserted 0.93 |
| s1 | Small amplitude fluctuations have similar dynamics in both theories for frequencies far below the pair breaking threshold and wave vectors much smaller than the Fermi momentum, and the low frequency linear responses match well for surprisingly large wave vectors, even up to the Fermi momentum. | result 1.00 | 0.87 | 0.20 | asserted 1.00 |
| s2 | For non-linear dynamics such as vortex generation, the ETF provides a semi-quantitative description of SLDA dynamics as long as the fluctuations do not have significant power near the pair breaking threshold, otherwise the dynamics of the ETF cannot be trusted. | result 0.86 | 0.89 | 0.47 | asserted 0.97 |
| s3 | Nonlinearities in the ETF tends to generate high-frequency fluctuations, and with no normal component to remove this energy from the superfluid, features like vortex lattices cannot relax and crystallize as they do in the SLDA. | interpretation 0.69 | 0.79 | 0.13 | asserted 0.97 |
| s4 | We present a heuristic diagnostic for validating the reliability of ETF dynamics by considering the approximate conservation of square of the gap: $\int|\Delta|^2$. | contribution 0.70 | 0.91 | 0.20 | asserted 0.93 |
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The paper
Original abstract
We present a comparison between simulated dynamics of the unitary fermion gas using the superfluid local density approximation (SLDA) and a simplified bosonic model, the extended Thomas Fermi (ETF) with a unitary equation of state. Small amplitude fluctuations have similar dynamics in both theories for frequencies far below the pair breaking threshold and wave vectors much smaller than the Fermi momentum, and the low frequency linear responses match well for surprisingly large wave vectors, even up to the Fermi momentum. For non-linear dynamics such as vortex generation, the ETF provides a semi-quantitative description of SLDA dynamics as long as the fluctuations do not have significant power near the pair breaking threshold, otherwise the dynamics of the ETF cannot be trusted. Nonlinearities in the ETF tends to generate high-frequency fluctuations, and with no normal component to remove this energy from the superfluid, features like vortex lattices cannot relax and crystallize as they do in the SLDA. We present a heuristic diagnostic for validating the reliability of ETF dynamics by considering the approximate conservation of square of the gap: $\int|\Delta|^2$.
Human review
How the literature uses it
5 arXiv papers cite this in 6 sentences
Papers citing it · 3 sentences without a confident label
Uses its method or tool 1 paper
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We validate our procedure using a dynamical ETF model [ref] , equivalent to a GPE for bosonic “dimers” $m_B = 2m$ of fermionic pairs, with an equation of state $ℰ(n) ∝ξρ^5/3$ characterized by the Bertsch parameter $ξ≈0.37$ tuned to consistently fit both QMC and experimental results [ref] .
Strength of the Vortex-Pinning Interaction from Real-Time Dynamics · Introduction · 0.86
Cites it as support 1 paper
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Despite the computational simplicity of the ETF model, it has been demonstrated to quantitatively reproduce a range of low-energy dynamics of both UFG experiments [ref] and fermionic DFT simulations [ref] .
Strength of the Vortex-Pinning Interaction from Real-Time Dynamics · Introduction · 0.98
Cites it as background 1 paper
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The advantages and the limits of this approach have been widely discussed in the literature (see for instance the recent discussion in [ref] , and references therein).
Josephson oscillations and self-trapping of superfluid fermions in a double-well potential · Large oscillations and self-trapping · 0.99
What it cites · 42 sentences without a confident label
Contests 1 paper
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Note, however, that the difference in dynamics here is in contrast with the implied claim of Refs. [ref] that the coarse graining is simply needed to replicate the averaging implied by imaging.
Shock waves in strongly interacting Fermi gas from time-dependent density functional calculations · Nonlinear Response · contest 0.78
Uses data or values from 2 papers
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The current best fit value $ξ=0.3742(5)$ is obtained by consistently fitting both QMC and experimental results [ref] with a self-consistent fermionic DFT called the SLDA.
Effective-Range Dependence of Resonantly Interacting Fermions · Introduction · 0.94
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The value for $≈1.5(3)$ follows from an analysis of gradient corrections to harmonically trapped gases [ref] .
The Unitary Fermi Gas in a Harmonic Trap and its Static Response · Linear Response · 0.87
Compares with 2 papers
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This is qualitatively consistent with estimate of these parameters from the $ϵ$-expansion [ref] (expanding in spatial dimension: $ϵ= 4 - d$) which finds $≈8/5 + (ϵ^2)$ and $≈c_ω+ (ϵ^2)$.[To compare with [ref] , note that their $c_s≡/2ξ$.] The BdG mean-field theory [ref] finds quite different values, $= 7/3$ and $c_ω= 0.7539$.
Density Functional Theory for non-relativistic Fermions in the Unitarity Limit · Linear Response · 0.94
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This is qualitatively consistent with estimate of these parameters from the $ϵ$-expansion [ref] (expanding in spatial dimension: $ϵ= 4 - d$) which finds $≈8/5 + (ϵ^2)$ and $≈c_ω+ (ϵ^2)$.[To compare with [ref] , note that their $c_s≡/2ξ$.] The BdG mean-field theory [ref] finds quite different values, $= 7/3$ and $c_ω= 0.7539$.
Effective theory for the Goldstone field in the BCS-BEC crossover at T=0 · Linear Response · 0.94
Cites as support 3 papers
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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] .
Shock waves in strongly interacting Fermi gas from time-dependent density functional calculations · The ETF Model · 0.97
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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] .
The Unitary Fermi Gas in a Harmonic Trap and its Static Response · The ETF Model · 0.97
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As argued in [ref] , the transverse response should be positive to ensure stability with respect to a spontaneous generation of currents or formation of inhomogeneous condensates.
General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas · Linear Response · 0.98
Cites as background 21 papers
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TDSLDA The time-dependent generalization of the SLDA (TDSLDA) provides a model for directly studying time-dependent phenomena in the UFG (see [ref] for a review).
Time-Dependent Superfluid Local Density Approximation · Introduction · 0.97
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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).
Resonantly Interacting Fermions In a Box · The SLDA · 0.90
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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).
Local Density Functional Theory for Superfluid Fermionic Systems: The Unitary Gas · The SLDA · 0.90
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