Some open questions in TDDFT: Clues from Lattice Models and Kadanoff-Baym Dynamics

摘要

Two aspects of TDDFT, the linear response approach and the adiabatic localdensity approximation, are examined from the perspective of lattice models. Tothis end, we review the DFT formulations on the lattice and give a concisepresentation of the time-dependent Kadanoff-Baym equations, used to asses thelimitations of the adiabatic approximation in TDDFT. We present results for thedensity response function of the 3D homogeneous Hubbard model, and point out adrawback of the linear response scheme based on the linearized Sham-Schl\"uterequation. We then suggest a prescription on how to amend it. Finally, weanalyze the time evolution of the density in a small cubic cluster, and compareexact, adiabatic-TDDFT and Kadanoff-Baym-Equations densities. Our results showthat non-perturbative (in the interaction) adiabatic potentials can performquite well for slow perturbations but that, for faster external fields, memoryeffects, as already present in simple many-body approximations, are clearlyrequired.