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

Roberto D’Agosta and Massimiliano Di Ventra

Phys. Rev. B 87, 155129 – Published 15 April 2013

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. 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, which applies to any density functional theory, showing that it must fulfill certain “dimensionality” requirements.

Received 15 October 2012

DOI:https://doi.org/10.1103/PhysRevB.87.155129

Authors & Affiliations

Roberto D’Agosta^*

ETSF Scientific Development Center, Departamento de Física de Materiales, Universidad del País Vasco, E-20018 San Sebastián, Spain and IKERBASQUE, Basque Foundation for Science, E-48011, Bilbao, Spain

Massimiliano Di Ventra^†