Time-dependent current density functional theory via time-dependent deformation functional theory: A constrained search formulation in the time domain

TL;DR

This paper reformulates time-dependent current density functional theory (TDCDFT) using a constrained search approach inspired by time-dependent deformation functional theory (TDDefFT), clarifying the origin and causal structure of the fundamental functionals.

Contribution

It introduces a constrained search formulation of TDCDFT based on TDDefFT, avoiding traditional potential-to-density mappings and clarifying the functionals' physical origin.

Findings

Universal functionals derived from a constrained many-body problem.

Clarification of the causal structure of the functionals.

Enhanced predictive power of TDCDFT through this formulation.

Abstract

The logical structure and the basic theorems of time-dependent current density functional theory (TDCDFT) are analyzed and reconsidered from the point of view of recently proposed time-dependent deformation functional theory (TDDefFT). It is shown that the formalism of TDDefFT allows to avoid a traditional external potential-to-density/current mapping. Instead the theory is formulated in a form similar to the constrained search procedure in the ground state DFT. Within this formulation of TDCDFT all basic functionals appear from the solution of a constrained universal many-body problem in a comoving reference frame, which is equivalent to finding a conditional extremum of a certain universal action functional. As a result the physical origin of the universal functionals entering the theory, as well as their proper causal structure becomes obvious. In particular, this leaves no room for any doubt concerning predictive power of the theory.