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arXiv · 2408.00009

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

Mi-Song Dupuy·Eloïse Letournel·Antoine Levitt
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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.

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Mi-Song Dupuy, Eloïse Letournel, Antoine Levitt. 2024-07-24. Linear response and resonances in adiabatic time-dependent density functional theory. https://arxiv.org/abs/2408.00009

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