Time-Dependent Superfluid Local Density Approximation

Aurel Bulgac; Michael McNeil Forbes

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Time-Dependent Superfluid Local Density Approximation

Aurel Bulgac, Michael McNeil Forbes

Quantum Gases · Submitted 10 Jan 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Unlike linear response theory, which is only valid for weak external fields, the (TDSLDA) approach allows one to study non-linear excitations in fermionic superfluids, including large amplitude collective modes, and the response to strong external probes.

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The paper's own sentences, arranged. 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.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.78 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The time-dependent superfluid local density approximation (TDSLDA) is an extension of the Hohenberg-Kohn density functional theory (DFT) to time-dependent phenomena in superfluid fermionic systems. Unlike linear response theory, which is only valid for weak external fields, the (TDSLDA) approach allows one to study non-linear excitations in fermionic superfluids, including large amplitude collective modes, and the response to strong external probes. Even in the case of weak external fields, the (TDSLDA) approach is technically easier to implement. We will illustrate the implementation of the (TDSLDA) for the unitary Fermi gas, where dimensional arguments and Galilean invariance simplify the form of the functional, and ab initio input from (QMC) simulations fix the coefficients to quite high precision.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The time-dependent superfluid local density approximation (TDSLDA) is an extension of the Hohenberg-Kohn density functional theory (DFT) to time-dependent phenomena in superfluid fermionic systems.	background 0.68	0.11	0.09	asserted 1.00
s1	Unlike linear response theory, which is only valid for weak external fields, the (TDSLDA) approach allows one to study non-linear excitations in fermionic superfluids, including large amplitude collective modes, and the response to strong external probes.	contribution 0.38	0.15	0.20	asserted 0.98
s2	Even in the case of weak external fields, the (TDSLDA) approach is technically easier to implement.	background 0.34	0.26	0.07	asserted 1.00
s3	We will illustrate the implementation of the (TDSLDA) for the unitary Fermi gas, where dimensional arguments and Galilean invariance simplify the form of the functional, and ab initio input from (QMC) simulations fix the coefficients to quite high precision.	method 0.51	0.80	0.11	asserted 0.97

What kind of paper the classifier reports this is: method or tool 0.96 · evidence from argument 0.59.

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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

The paper

Original abstract

The time-dependent superfluid local density approximation (TDSLDA) is an extension of the Hohenberg-Kohn density functional theory (DFT) to time-dependent phenomena in superfluid fermionic systems. Unlike linear response theory, which is only valid for weak external fields, the (TDSLDA) approach allows one to study non-linear excitations in fermionic superfluids, including large amplitude collective modes, and the response to strong external probes. Even in the case of weak external fields, the (TDSLDA) approach is technically easier to implement. We will illustrate the implementation of the (TDSLDA) for the unitary Fermi gas, where dimensional arguments and Galilean invariance simplify the form of the functional, and ab initio input from (QMC) simulations fix the coefficients to quite high precision.

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1 arXiv paper cite this in 2 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

Cites it as background 1 paper

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).

Validating Simple Dynamical Simulations of the Unitary Fermi Gas · Introduction · 0.97

What it cites · 7 sentences without a confident label

Uses the method or tool of 3 papers

The homogeneous equations can then be used to translate this into a position dependent $Λ(r)$ that may be used in the previous equations and which has very good convergence properties [ref] (see also [ref] ):

The Unitary Fermi Gas: From Monte Carlo to Density Functionals · The Functional · 0.84
The homogeneous equations can then be used to translate this into a position dependent $Λ(r)$ that may be used in the previous equations and which has very good convergence properties [ref] (see also [ref] ):

Renormalization of the Hartree-Fock-Bogoliubov Equations in the Case of a Zero Range Pairing Interaction · The Functional · 0.84
As a result, a memory limited implementation of Broyden's method [ref] works well to accelerate convergence, thereby determining equilibrium configurations to use as an initial state for a subsequent time-dependent simulation.

Broyden's Method in Nuclear Structure Calculations · Technical Notes · 0.95

Cites as background 2 papers

Although exact in principle, there is no simple prescription for computing an exact density functional in a non-perturbative theory (see [ref] for recent discussions), and one must first formulate an approximate functional that captures the relevant physics.

Toward ab initio density functional theory for nuclei · Introduction · 0.87
In nuclear physics Galilean invariance have been considered for quite some time [ref] , and the contribution of these currents is often essential for describing the properties of excited states.

TDDFT with Skyrme Forces: Effect of Time-Odd Densities on Electric Giant Resonances · The Functional · 0.87

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