Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results

TL;DR

This paper clarifies foundational aspects of stochastic time-dependent current-density functional theory for open quantum systems, addressing misunderstandings and highlighting potential pitfalls in recent formulations, with a focus on the potential mapping consistency.

Contribution

It provides rigorous clarification of the theory's foundational principles and identifies issues in recent attempts to improve the framework.

Findings

Identifies misunderstandings in the existing theory.

Shows inconsistencies in recent formulations.

Establishes dimensionality requirements for potential mapping.

Abstract

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.