Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0006356 · Physical Review A

Comment on “Analysis of causality in time-dependent density-functional theory”

M. Ya. Amusia, Vasily R. Shaginyan

Published Apr 11, 2001• 9 citations
arXivHTMLPDF

Abstract

It has been argued that there exists only one inverse of the linear-response function $\ensuremath{\chi},$ i.e., ${\ensuremath{\chi}}^{\ensuremath{-}1},$ which depends symmetrically on its spatial-times variables [M. K. Harbola and A. Banerjee, Phys. Rev. A 60, 5101 (1999)]. Some brief comments on this consideration are presented here. We show in contrast to Harbola and Banerjee, that it is possible to construct the causal inverse also. At the same time, we confirm the main statement of [Harbola and Banerjee] that in fact there is no contradiction between the symmetry and causality.

DOI
10.1103/physreva.63.056501

Related papers

Analysis of causality in time-dependent density-functional theory

Manoj K. Harbola, Arup Banerjee

It is pointed out that the kernel of the inverse response function $\ensuremath{\delta}v(\mathbf{r},t)/\ensuremath{\delta}\ensuremath{\rho}({\mathbf{r}}^{\ensuremath{'}}{,t}^{\ensuremath{'}}),$ whose existence is guaranteed by the Runge-Gross theorem, cannot vanish for $t<{t}^{\ensuremath{'}}.$ As such the kernel ${f}_{\mathrm{xc}},$ which is the functional derivative of the time-dependent exchange-correlation potential with respect to the density, can be symmetric with respect to an interchange between t and ${t}^{\ensuremath{'}}$ without violating causality. Thus there is no conflict between the symmetry requirement of this kernel and causality in time-dependent density-functional theory.

Physical Review A•Dec 1, 1999•15 citations

Causality and Symmetry in Time-Dependent Density-Functional Theory

Robert van Leeuwen

We resolve an existing paradox regarding the causality and symmetry properties of response functions within time-dependent density-functional theory. We do this by defining a new action functional within the Keldysh formalism. By functional differentiation the new functional leads to response functions which are symmetric in the Keldysh time contour parameter, but which become causal when a transition to physical time is made. The new functional is further used to derive the equations of the time-dependent optimized potential method.

Physical Review Letters•Feb 9, 1998•290 citations

Comment on “Modifying the variational principle in the action-integral-functional derivation of time-dependent density-functional theory”

Giovanni Vignale

In a paper recently published in Phys. Rev. A [arXiv:1010.4223], Schirmer has criticized an earlier work of mine [arXiv:0803.2727], as well as the foundations of time-dependent density functional theory. In Ref.[2], I showed that the so-called "causality paradox" - i.e., the failure of the exchange-correlation potential derived from the Runge-Gross time-dependent variational principle to satisfy causality requirements - can be solved by a careful reformulation of that variational principle. Fortunately, the criticism presented in Ref.[1] is based on elementary misunderstandings of the nature of functionals, gauge transformations, and the time-dependent variational principle. In this Comment I wish to point out and clear these misunderstandings.

arXiv:1103.5702•Physical Review A•Apr 27, 2011•5 citations

Reply to "Comment on 'Modifying the variational principle in the action-integral-functional derivation of time-dependent density functional theory'"

J. Schirmer

In a recent paper [Phys. Rev. A 77, 062511 (2008)], it was advocated to modify the variational principle for the action-integral functional in the Runge-Gross foundation of time-dependent density-functional theory. This was criticised in a subsequent paper [Phys. Rev. A 62, 052510 (2010)] by the present author. In a Comment [Phys. Rev. A 83, 046501 (2011)], it is argued that the criticism is unfounded. This is a response as given to the four specific points raised in the Comment, clarifying and confirming the essence of the original criticism.

arXiv:1105.2718•May 13, 2011•0 citations

Reply to “Comment on ‘Analysis of causality in time-dependent density-functional theory’ ”

Manoj K. Harbola

By employing the equation derived by Amusia and Shaginyan in their comment on our work, we show that the potential corresponding to a time-dependent density is a noncausal functional of the density. We further strengthen this conclusion on the basis of the exact equation satisfied by the density.

Physical Review A•Apr 11, 2001•2 citations

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

Roberto D’Agosta, Massimiliano Di Ventra

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.

arXiv:0911.3932•Nov 19, 2009•2 citations
It has been argued that there exists only one inverse of the linear-response function \ensuremathχ,\ensuremath{\chi},\ensuremathχ, i.e., \ensuremathχ\ensuremath−1,{\ensuremath{\chi}}^{\ensuremath{-}1},\ensuremathχ\ensuremath−1, which depends symmetrically on its spatial-times variables [M. K. Harbola and A. Banerjee, Phys. Rev. A 60, 5101 (1999)]. Some brief comments on this consideration are presented here. We show in contrast to Harbola and Banerjee, that it is possible to construct the causal inverse also. At the same time, we confirm the main statement of [Harbola and Banerjee] that in fact there is no contradiction between the symmetry and causality.
It is pointed out that the kernel of the inverse response function $\ensuremath{\delta}v(\mathbf{r},t)/\ensuremath{\delta}\ensuremath{\rho}({\mathbf{r}}^{\ensuremath{'}}{,t}^{\ensuremath{'}}),$ whose existence is guaranteed by the Runge-Gross theorem, cannot vanish for $t<{t}^{\ensuremath{'}}.$ As such the kernel fxc,{f}_{\mathrm{xc}},fxc​, which is the functional derivative of the time-dependent exchange-correlation potential with respect to the density, can be symmetric with respect to an interchange between t and ${t}^{\ensuremath{'}}$ without violating causality. Thus there is no conflict between the symmetry requirement of this kernel and causality in time-dependent density-functional theory.
We resolve an existing paradox regarding the causality and symmetry properties of response functions within time-dependent density-functional theory. We do this by defining a new action functional within the Keldysh formalism. By functional differentiation the new functional leads to response functions which are symmetric in the Keldysh time contour parameter, but which become causal when a transition to physical time is made. The new functional is further used to derive the equations of the time-dependent optimized potential method.
In a paper recently published in Phys. Rev. A [arXiv:1010.4223], Schirmer has criticized an earlier work of mine [arXiv:0803.2727], as well as the foundations of time-dependent density functional theory. In Ref.[2], I showed that the so-called "causality paradox" - i.e., the failure of the exchange-correlation potential derived from the Runge-Gross time-dependent variational principle to satisfy causality requirements - can be solved by a careful reformulation of that variational principle. Fortunately, the criticism presented in Ref.[1] is based on elementary misunderstandings of the nature of functionals, gauge transformations, and the time-dependent variational principle. In this Comment I wish to point out and clear these misunderstandings.
In a recent paper [Phys. Rev. A 77, 062511 (2008)], it was advocated to modify the variational principle for the action-integral functional in the Runge-Gross foundation of time-dependent density-functional theory. This was criticised in a subsequent paper [Phys. Rev. A 62, 052510 (2010)] by the present author. In a Comment [Phys. Rev. A 83, 046501 (2011)], it is argued that the criticism is unfounded. This is a response as given to the four specific points raised in the Comment, clarifying and confirming the essence of the original criticism.
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.