A unified approach to the density-potential mapping in a family of time-dependent density functional theories

Details A unified approach to the density-potential mapping in a family of time-dependent density functional theories A unified approach to the density-potential mapping in a family of time-dependent density functional theories

2011-01-11

arxiv.org/abs/1101.2166v1

Chemical Physics 391, 78 (2011)

Physics

Condensed Matter

Strongly Correlated Electrons

RevTeX4, 15 pages

Scientific paper

10.1016/j.chemphys.2011.04.005

It is shown that the density-potential mapping and the ${\cal V}$-representability problems in the time-dependent current density functional theory (TDCDFT) are reduced to the solution of a certain many-body nonlinear Schr\"odinger equation (NLSE). The derived NLSE for TDCDFT adds a link which bridges the earlier NLSE-based formulations of the time-dependent deformation functional theory (TDDefFT) and the time-dependent density functional theory (TDDFT). We establish close relations between the nonlinear many-body problems which control the existence of TDCDFT, TDDFT, and TDDefFT, and thus develop a unified point of view on the whole family of the TDDFT-like theories.

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