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

TL;DR

This paper demonstrates that the core problems in time-dependent current density functional theory can be reduced to solving a nonlinear Schrödinger equation, unifying various TDDFT-like theories through a common framework.

Contribution

It introduces a unified nonlinear Schrödinger equation approach that links TDCDFT, TDDFT, and TDDefFT, providing a comprehensive perspective on their interrelations.

Findings

Reduced density-potential mapping to a nonlinear Schrödinger equation

Established connections between TDCDFT, TDDFT, and TDDefFT

Unified framework for TDDFT-like theories

Abstract

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.