On the Kohn-Sham Approach to Time-Dependent Problems in a Density-Functional Framework

TL;DR

This paper analyzes the predictivity of the Kohn-Sham approach in time-dependent density functional theory, revealing limitations and the need for additional functionals and current information for accurate modeling.

Contribution

It extends and revises existing arguments on the predictivity of the Kohn-Sham method, highlighting the necessity of extra unknown functionals and current data.

Findings

Predictivity may require extra unknown functionals.

The Hartree-exchange-correlation potential is not uniquely determined by densities and initial states.

Current divergence influences the identification of the potential.

Abstract

Predictivity of the Kohn-Sham approach to dynamical problems, when regarded as an initial value problem in a time-dependent density functional framework, is analysed for a class of models for which the argument devised in the work of Maitra et al. (Phys. Rev. A 78, 056501 (2008), arXiv:cond-mat/0710.0018) for the standard electronic many-body problem does not apply. The original argument is here extended and revised. As a result, predictivity for this class of problems seems possible only at the price of introducing extra unknown functionals in the corresponding Kohn-Sham equation. Furthermore, the same argument, when applied to original electronic problem, suggests that the Hartree-exchange-correlation potential is not unambiguously identified by the contemporary and past densities and initial states, but also requires knowledge of the divergence of the contemporary Kohn-Sham current.