2026-09-22 フランス国立科学研究センター（CNRS）
©Andrea Cavalleri / MPSD / MPG
＜関連情報＞
- https://news.cnrs.fr/articles/solving-the-schrodinger-equation-with-imagination
- https://journals.aps.org/prl/abstract/10.1103/xtjx-r2lm
- https://journals.aps.org/pra/abstract/10.1103/w2bz-p8df
幾何学的時間依存密度汎関数理論 Geometric Time-Dependent Density Functional Theory
Éric Cancès, Théo Duez, Jari van Gog, Asbjørn Bækgaard Lauritsen, Mathieu Lewin, and Julien Toulouse
Physical Review Letters 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.
有限格子上の時間依存密度汎関数理論への応用を伴う、制約付きシュレディンガー力学の幾何学的理論 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
Physical Review A Published: 24 June, 2026
DOI: https://doi.org/10.1103/w2bz-p8df
Abstract
Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we revisit the foundations of TDDFT within a finite-dimensional setting by developing a general geometric framework for Schrödinger dynamics subject to prescribed expectation values of selected observables. We show that multiple natural definitions of such constrained dynamics arise from the underlying geometry of the state manifold. The conventional TDDFT formulation emerges from demanding stationarity of the action functional, while an alternative, purely geometric construction leads to a distinct form of constrained Schrödinger evolution. This alternative dynamics may provide a more mathematically robust route to TDDFT and may suggest alternative strategies for constructing nonadiabatic approximations. Applying the theory to interacting fermions on finite lattices, we derive Kohn-Sham schemes in which the density constraint is enforced via an imaginary potential or, equivalently, a nonlocal Hermitian operator. Numerical illustrations for the Hubbard dimer demonstrate the behavior of these approaches.
