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Geometric Time-Dependent Density Functional Theory

Éric Cancès1,2,*, Théo Duez1,2,†, Jari van Gog3,‡, Asbjørn Bækgaard Lauritsen4,§, Mathieu Lewin4,∥, and Julien Toulouse3,¶

  • *Contact author: eric.cances@enpc.fr
  • †Contact author: theo.duez@enpc.fr
  • ‡Contact author: jari.van_gog@etu.sorbonne-universite.fr
  • §Contact author: lauritsen@ceremade.dauphine.fr
  • ∥Contact author: Mathieu.Lewin@math.cnrs.fr
  • Contact author: toulouse@lct.jussieu.fr
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Phys. Rev. Lett. 136, 256401 – Published 24 June, 2026

DOI: https://doi.org/10.1103/xtjx-r2lm

Abstract

We provide a new formulation of time-dependent density functional theory (TDDFT) based on the geometric structure of the set of states constrained to have a fixed density. Orbital-free TDDFT is formulated using a hydrodynamics equation involving a new density-to-current functional map. In the corresponding Kohn-Sham equation, the density is reproduced using a nonlocal operator. Finally, we present numerical simulations for one-dimensional soft-Coulomb systems.

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synopsis

Transforming the Computational Workhorse of Electronic Structure

Published 24 June, 2026

A geometric reformulation of time-dependent density-functional theory better describes nonequilibrium systems.

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Geometric theory of constrained Schrödinger dynamics with application to time-dependent density-functional theory on a finite lattice

Éric Cancès, Théo Duez, Jari van Gog, Asbjørn Bækgaard Lauritsen, Mathieu Lewin, and Julien Toulouse
Phys. Rev. A 113, 062222 (2026)

Article Text

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Phys. Rev. Lett. 136, 256401– Published 24 June, 2026
  • Received 12 January 2026
  • Accepted 6 May 2026
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