Linear response and resonances in adiabatic time-dependent density functional theory - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

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

Résumé

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.
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Dates et versions

hal-04659092 , version 1 (23-07-2024)
hal-04659092 , version 2 (17-09-2024)

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Mi-Song Dupuy, Eloïse Letournel, Antoine Levitt. Linear response and resonances in adiabatic time-dependent density functional theory. 2024. ⟨hal-04659092v2⟩
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