English

Linear response and resonances in adiabatic time-dependent density functional theory

Analysis of PDEs 2024-09-19 v2

Abstract

We consider the electrons of a molecule in the adiabatic time-dependent density functional theory approximation. We establish the well-posedness of the time evolution and its linear response close to a non-degenerate ground state, and prove the appearance of resonances at relevant frequencies. The main mathematical difficulty is due to the structure of the linearized equations, which are not complex-linear. We bypass this difficulty by reformulating the linearized problem as a real Hamiltonian system, whose stability is ensured by the second-order optimality conditions on the energy.

Keywords

Cite

@article{arxiv.2408.00009,
  title  = {Linear response and resonances in adiabatic time-dependent density functional theory},
  author = {Mi-Song Dupuy and Eloïse Letournel and Antoine Levitt},
  journal= {arXiv preprint arXiv:2408.00009},
  year   = {2024}
}
R2 v1 2026-06-28T17:59:38.491Z