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

Abstract

It is shown that the density-potential mapping and the V -representability problems in the time-dependent current density functional theory (TDCDFT) are reduced to the solution of a certain many-body nonlinear Schrödinger equation (NLSE). The derived NLSE for TDCDFT links the earlier NLSE-based formulations of the time-dependent deformation functional theory (TDDefFT) and the time-dependent density functional theory (TDDFT). We establish a close relation 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-type theories.