Comment on ``Time-dependent current-density functional theory for generalized open quantum systems" by J. Yuen-Zhou, C. Rodriiguez-Rosario and A. Aspuru-Guzik

TL;DR

This paper critically analyzes a recent extension of time-dependent current density functional theory for open quantum systems, highlighting mathematical inaccuracies and questioning the physical validity of certain assumptions.

Contribution

It provides a critical commentary on the theoretical foundations of the extended TDCDFT, identifying errors and challenging the physical relevance of some conditions used in the original proof.

Findings

Identifies incorrect statements in the original theorems.

Shows the introduction of an arbitrary, non-physical condition in the proof.

Argues that different vector potentials can produce identical physical dynamics.

Abstract

We comment on a recent paper by Yuen-Zhou et al. [ Phys. Chem. Chem. Phys. 2009, 11, 4509 ] which extends some of the results of Time-Dependent Current Density Functional Theory applied to open quantum systems. Besides pointing out some incorrect statements in the theorems, we show that in the proof of the main result of the paper an arbitrary condition is introduced. Moreover, we argue that, since this condition has not a physical origin, one can find two systems with different vector potentials that lead to the same dynamics of the physical quantities of interest, the current and particle densities.