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:1105.2718

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

J. Schirmer

Published May 13, 2011• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1105.2718

Related papers

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

Reexamination of the Runge-Gross action-integral functional

J. Schirmer

The density-based action-integral functional introduced by Runge and Gross [Phys. Rev. Lett. 52, 997 (1984)] in their foundation of time-dependent density-functional theory is reexamined. Based on a simple expansion of the original definition, it becomes apparent that the action-integral functional is a trivial construct and, moreover, nonstationary. It cannot be used to establish equations of motion for the time evolution of quantum systems at the density-function level.

arXiv:1203.5052•Physical Review A•Jul 26, 2012•7 citations

Reply to “Comment on ‘Critique of the foundations of time-dependent density-functional theory’ ”

J. Schirmer, Andreas Dreuw

In the preceding Comment, Maitra, van Leeuwen, and Burke (MLB) [Phys. Rev. A 78, 056501 (2008) attempt to refute our criticism of the foundations of time-dependent density functional theory [see J. Schirmer and A. Dreuw, Phys. Rev. A 75, 022513 (2007)]. However, their arguments miss the essence of our position. This is partly due to an ambiguity concerning the present status of the time-dependent (TD) Kohn-Sham (KS) equations. Based on the first Runge-Gross (mapping) theorem, the TD KS equations have to be established as a fixed-point iteration scheme for potential functionals (PF-FPI). Here, however, the convergence of the FPI is not assured. On the other hand, time propagation of the TD KS equations in their PF-FPI form fails because these equations do not represent physical equations of motion. MLB present a construction of the exact exchange-correlation potential, apparently contradicting one of our findings. We explain that their construction is explicitly based on the solution of the TD Schr\"odinger equation and, for this reason, does not address our objections, let alone refute them.

arXiv:0803.4172•Physical Review A•Nov 3, 2008•39 citations

Action formalism of time-dependent density-functional theory

Martín A. Mosquera

The Runge-Gross [E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984)] action functional of time-dependent density-functional theory leads to a well-known causality paradox; that is, a perturbation of the electronic density in the future affects the response of the system in the present. This paradox is known to be caused by an inconsistent application of the Dirac-Frenkel variational principle. In view of the recent solutions to this problem, the action functional employed by Runge and Gross in their formulation of time-dependent density-functional theory is analyzed in the context of the Keldysh contour technique. The time-dependent electronic density and the concept of causality are extended to the contour. We derive a variational equation that obeys causality and relates the exchange-correlation potential with its kernel and the functional derivative of the exchange-correlation action functional with respect to the density. It is shown that the adiabatic local-density approximation is a consistent solution of this equation and that the time-dependent optimized potential method can also be derived from it. The formalism presented here can be used to find new approximation methods for the exchange-correlation potential and to avoid the causality dilemma.

arXiv:1303.5679•Physical Review A•Aug 26, 2013•6 citations

Reply to "Comment on 'Modified quantum-speed-limit bounds for open quantum dynamics in quantum channels'"

Xin Liu, Wei Wu, Chao Wang

The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.

arXiv:1805.01986•May 5, 2018•0 citations

Reply to “Comment on ‘Coherent-state path integrals in the continuum’”

G. Kordas, S. I. Mistakidis, A. I. Karanikas

In this Reply we briefly clarify the main points of our method to construct coherent-state path integrals in the continuum and we reply to the critique raised by in the preceding Comment by Kochetov [Phys. Rev. A 99, 026101 (2019)]. By using definite examples, we prove that our approach is capable of resolving the inconsistencies accompanying the standard coherent-state path-integral representation of interacting systems.

Physical Review A•Feb 13, 2019•3 citations
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.
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 the preceding Comment, Maitra, van Leeuwen, and Burke (MLB) [Phys. Rev. A 78, 056501 (2008) attempt to refute our criticism of the foundations of time-dependent density functional theory [see J. Schirmer and A. Dreuw, Phys. Rev. A 75, 022513 (2007)]. However, their arguments miss the essence of our position. This is partly due to an ambiguity concerning the present status of the time-dependent (TD) Kohn-Sham (KS) equations. Based on the first Runge-Gross (mapping) theorem, the TD KS equations have to be established as a fixed-point iteration scheme for potential functionals (PF-FPI). Here, however, the convergence of the FPI is not assured. On the other hand, time propagation of the TD KS equations in their PF-FPI form fails because these equations do not represent physical equations of motion. MLB present a construction of the exact exchange-correlation potential, apparently contradicting one of our findings. We explain that their construction is explicitly based on the solution of the TD Schr\"odinger equation and, for this reason, does not address our objections, let alone refute them.
The Runge-Gross [E. Runge and E. K. U. Gross, Phys. Rev. Lett. 52, 997 (1984)] action functional of time-dependent density-functional theory leads to a well-known causality paradox; that is, a perturbation of the electronic density in the future affects the response of the system in the present. This paradox is known to be caused by an inconsistent application of the Dirac-Frenkel variational principle. In view of the recent solutions to this problem, the action functional employed by Runge and Gross in their formulation of time-dependent density-functional theory is analyzed in the context of the Keldysh contour technique. The time-dependent electronic density and the concept of causality are extended to the contour. We derive a variational equation that obeys causality and relates the exchange-correlation potential with its kernel and the functional derivative of the exchange-correlation action functional with respect to the density. It is shown that the adiabatic local-density approximation is a consistent solution of this equation and that the time-dependent optimized potential method can also be derived from it. The formalism presented here can be used to find new approximation methods for the exchange-correlation potential and to avoid the causality dilemma.
The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the inconsistency presented in our paper is not a same one to which is presented by the authors of the comment, it exists and be unavoidable in their example. Accordingly, we believe the result in our paper is usable in numerical calculations.