Runge-Gross action-integral functional re-examined

TL;DR

This paper critically re-examines the Runge-Gross action-integral functional in TDDFT, revealing it as trivial and non-stationary, thus challenging its role in deriving equations of motion for quantum systems.

Contribution

It provides a fundamental re-evaluation of the original functional, showing its limitations and implications for the foundations of TDDFT.

Findings

The action-integral functional is trivial and non-stationary.

It cannot be used to derive equations of motion in TDDFT.

The original functional's limitations are clarified.

Abstract

The density-based action-integral functional introduced by Runge and Gross [Phys. Rev. Lett. 52, 997(1984)] in their foundation of time-dependent density-functional theory (TDDFT) is re-examined. Based on an obvious expansion of the original definition, it becomes apparent that the action-integral functional is both trivial and non-stationary. It cannot be used to establish equations of motion for the time-evolution of quantum systems at the density-function level.