Brief review related to the foundations of time-dependent density functional theory

TL;DR

This paper reviews the theoretical foundations of time-dependent density functional theory, focusing on the derivation of electron density from potentials, the role of the Dirac density matrix, and issues of causality in linear response theory.

Contribution

It provides a conceptual review of the foundational equations and causality considerations in time-dependent density functional theory, including potential extraction methods.

Findings

Relation of the density to a generalized equation of motion involving the Dirac density matrix

Survey of linear response theory emphasizing causality issues

Proposal of methods to extract potentials for solvable models

Abstract

The electron density $n(\rb,t)$, which is the central tool of time-dependent density functional theory, is presently considered to be derivable from a one-body time-dependent potential $V(\rb,t)$, via one-electron wave functions satisfying a time- dependent Schr\"{o}dinger equation. This is here related via a generalized equation of motion to a Dirac density matrix now involving $t$. Linear response theory is then surveyed, with a special emphasis on the question of causality with respect to the density dependence of the potential. Extraction of $V(\rb,t)$ for solvable models is also proposed.