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Adiabatic approximation in time-dependent reduced-density-matrix functional theory

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Ryan Requist, Oleg Pankratov

Strongly Correlated Electrons · Submitted 5 Nov 2009

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

The authors' main claim Both types of resonances have the same origin -- the interference of dynamical and scattering phases.

how it is stated · asserted 1.00 read the record →

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arXiv ID0911.0945 (version 2)
Pith IDQZ6LE2XL, Pith's permanent record of this paper and its review
CitationOleg Pankratov, Ryan Requist. "Adiabatic approximation in time-dependent reduced-density-matrix functional theory." arXiv:0911.0945 (2009). https://pith.science/paper/QZ6LE2XL
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,641 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.68 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.16 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced-density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the occupation numbers of single-particle orbitals, are obtained from the constrained minimization of the instantaneous ground state energy functional rather than from their dynamical equations. To clarify the motivation for this minimization condition, we discuss a sequence of adiabatic energy functionals, each obeying a minimum principle. The performance of the approximation vis-a`-vis nonadiabatic effects is assessed in real-time simulations for a two-site Hubbard model. Due to the presence of Landau-Zener-type transitions, the system evolves into a nonstationary state with persistent oscillations in the observables. The amplitude and phase of the oscillations exhibit resonance behavior both with respect to the strength of the electron-electron interaction and the rate of variation of the external potential. Both types of resonances have the same origin -- the interference of dynamical and scattering phases.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced-density matrix (one-matrix). contribution 0.97 0.94 0.09 asserted 0.99
s1 The eigenvalues of the one-matrix, which represent the occupation numbers of single-particle orbitals, are obtained from the constrained minimization of the instantaneous ground state energy functional rather than from their dynamical equations. method 0.85 0.85 0.19 asserted 1.00
s2 To clarify the motivation for this minimization condition, we discuss a sequence of adiabatic energy functionals, each obeying a minimum principle. method 0.51 0.81 0.04 asserted 0.84
s3 The performance of the approximation vis-a`-vis nonadiabatic effects is assessed in real-time simulations for a two-site Hubbard model. method 0.80 0.93 0.06 asserted 0.95
s4 Due to the presence of Landau-Zener-type transitions, the system evolves into a nonstationary state with persistent oscillations in the observables. result 1.00 0.85 0.13 asserted 1.00
s5 The amplitude and phase of the oscillations exhibit resonance behavior both with respect to the strength of the electron-electron interaction and the rate of variation of the external potential. result 1.00 0.89 0.19 asserted 1.00
s6 Both types of resonances have the same origin -- the interference of dynamical and scattering phases. interpretation 0.96 0.81 0.21 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.98 · evidence from simulation or computation 1.00.

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  • references and citing sentences
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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

With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced-density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the occupation numbers of single-particle orbitals, are obtained from the constrained minimization of the instantaneous ground state energy functional rather than from their dynamical equations. To clarify the motivation for this minimization condition, we discuss a sequence of adiabatic energy functionals, each obeying a minimum principle. The performance of the approximation vis-a`-vis nonadiabatic effects is assessed in real-time simulations for a two-site Hubbard model. Due to the presence of Landau-Zener-type transitions, the system evolves into a nonstationary state with persistent oscillations in the observables. The amplitude and phase of the oscillations exhibit resonance behavior both with respect to the strength of the electron-electron interaction and the rate of variation of the external potential. Both types of resonances have the same origin -- the interference of dynamical and scattering phases.

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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

What it cites · 4 sentences without a confident label

Cites as support 1 paper
  • For such reconstructions the right-hand side of Eq. ([ref]) vanishes identically, [ref] so that the occupation numbers remain constant in time for any external potential $v(𝐫,t)$, regardless of its strength and rate of change.

    Time-dependent natural orbitals and occupation numbers · Adiabatic extension approximation · 0.98

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