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

The Journal of Chemical Physics

Reply to “Comment on ‘A quantum-classical bracket that satisfies the Jacobi identity’ ” [J. Chem. Phys. 124, 201104 (2006)]

Oleg V. Prezhdo

Published Feb 6, 2007• 4 citations
Publisher

Abstract

The argument made in the cited Comment is based on a calculation that was not intended in the original paper. Starting from a fully quantum expression, application of the ℏ→0 limit after every bracket calculation as stated in the paper retains consistent orders of ℏ and does obey the Jacobi identity.
DOI
10.1063/1.2431651

Related papers

Comment on “A quantum-classical bracket that satisfies the Jacobi identity” [J. Chem. Phys. 124, 201104 (2006)]

L. L. Salcedo

It shown that the quantum-classical dynamical bracket recently proposed in J. Chem. Phys. 124, 201104 (2006) fails to satisfy the Jacobi identity.

arXiv:quant-ph/0701054•The Journal of Chemical Physics•Feb 6, 2007•14 citations

Reply to the Comment on ‘The correspondence between quantum and classical mechanics: An experimental demonstration of the smooth transition between the two regimes’ [Chem. Phys. Lett. 402 (2005) 519]

Anthony J. Horsewill

Chemical Physics Letters•Nov 29, 2006•4 citations

Comment on “Equivalence of two approaches for quantum-classical hybrid systems” [J. Chem. Phys. 128, 204104 (2008)]

V. I. Gerasimenko

We discuss the links between consistent and approximate descriptions of the quantum-classical systems, i.e., systems composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum description.

arXiv:0909.4942•The Journal of Chemical Physics•Sep 28, 2009•1 citation

Reply to “Comment on ‘Arbitrated quantum-signature scheme’ ”

Guihua Zeng

To reply to the Comment on our original paper entitled ``Arbitrated quantum-signature scheme'' [Phys. Rev. A 65, 042312 (2002)], we present more detailed presentations and proofs of the quantum-signature scheme in our paper. We feel our further investigation has shown that the original quantum-signature scheme is secure and operationally well defined. In addition, proofs illustrate that the quantum-signature scheme with unknown quantum states is also suitable in principle.

Physical Review A•Jul 28, 2008•112 citations

A quantum-classical bracket that satisfies the Jacobi identity

Oleg V. Prezhdo

A quantum-classical bracket is proposed and is shown to satisfy the Jacobi identity, in contrast to previous definitions that obey this property only up to higher order terms in the Planck constant variant Planck's over 2pi. The Jacobi identity is required of a true Lie bracket and ensures that the Lie bracket of constants of motion is also a constant of motion. An explicit calculation of the Jacobi identity highlights the difference between the proposed and traditional definitions. A further example illustrates that the proposed bracket generates a more consistent quantum-classical dynamics than the traditional bracket. The traditional quantum-classical dynamics in the Henon-Heiles system diverges due to higher order variant Planck's over 2pi terms. The divergence is eliminated with the proposed bracket.

The Journal of Chemical Physics•May 22, 2006•35 citations

Response to “Comment on ‘Equivalence of two approaches for quantum-classical hybrid systems’ ” [J. Chem. Phys. 131, 127101 (2009)]

Fei Zhan, Yuan Lin, Biao Wu

The Journal of Chemical Physics•Sep 28, 2009•0 citations
A quantum-classical bracket is proposed and is shown to satisfy the Jacobi identity, in contrast to previous definitions that obey this property only up to higher order terms in the Planck constant variant Planck's over 2pi. The Jacobi identity is required of a true Lie bracket and ensures that the Lie bracket of constants of motion is also a constant of motion. An explicit calculation of the Jacobi identity highlights the difference between the proposed and traditional definitions. A further example illustrates that the proposed bracket generates a more consistent quantum-classical dynamics than the traditional bracket. The traditional quantum-classical dynamics in the Henon-Heiles system diverges due to higher order variant Planck's over 2pi terms. The divergence is eliminated with the proposed bracket.