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Physical Review A

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

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

Published Feb 13, 2019• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.99.026102

Related papers

Comment on “Coherent-state path integrals in the continuum”

E. A. Kochetov

Kordas et al. [Phys. Rev. A 90, 032104 (2014)] claim to have established a time-continuous formulation of the path integration in the coherent-state (CS) basis free from the inconsistency first reported by Wilson and Galitski [Phys. Rev. Lett. 106, 110401 (2011)]. Since a few recent investigations consider the approach advocated by Kordas et al. as providing a remedy for the CS path-integral anomaly, I feel it is appropriate to show that the formulation proposed by Kordas et al. does not eliminate the anomaly. The Reply does not change the status of my criticism.

arXiv:1811.10230•Physical Review A•Feb 13, 2019•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 a Comment on "Quantum Decoherence in Disordered Mesoscopic Systems" (cond-mat/9808078, cond-mat/9808053)

Dmitry S. Golubev, Andrei D. Zaikin

We reply to the critique of our results raised by Aleiner, Altshuler and Gershenzon (AAG) in cond-mat/9808078 and cond-mat/9808053. We demonstrate that our path integral analysis fully reproduces the results of AAG if analyzed on a perturbative level. This should settle the issue of "missing diagrams" in our calculation. We, furthermore, demonstrate that our approach allows us to proceed beyond the Golden-rule-type perturbation theory employed by AAG. This explains the difference between our and AAG's results. We also comment on the comparison of our results with the experiments presented by AAG.

arXiv:cond-mat/9811185•Nov 13, 1998•0 citations

Coherent-state path integrals in the continuum

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

We discuss the time continuous path integration in the coherent-state basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and nonperturbative approximations already known in the quantum-field-theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.

arXiv:1408.3210•Physical Review A•Sep 3, 2014•14 citations

Coherent-state path integrals in the continuum: The SU(2) case

G. Kordas, Dimitrios Kalantzis, A. I. Karanikas

We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.

arXiv:1605.06757•May 22, 2016•1 citation

Correct path-integral formulation of the quantum thermal field theory in the coherent state representation

Jun-Chen Su, Zheng Fu-Hou

This paper has been superseded by hep-th/0510131.

arXiv:hep-th/0506108•Jun 14, 2005•0 citations
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.
Kordas et al. [Phys. Rev. A 90, 032104 (2014)] claim to have established a time-continuous formulation of the path integration in the coherent-state (CS) basis free from the inconsistency first reported by Wilson and Galitski [Phys. Rev. Lett. 106, 110401 (2011)]. Since a few recent investigations consider the approach advocated by Kordas et al. as providing a remedy for the CS path-integral anomaly, I feel it is appropriate to show that the formulation proposed by Kordas et al. does not eliminate the anomaly. The Reply does not change the status of my criticism.
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.
We reply to the critique of our results raised by Aleiner, Altshuler and Gershenzon (AAG) in cond-mat/9808078 and cond-mat/9808053. We demonstrate that our path integral analysis fully reproduces the results of AAG if analyzed on a perturbative level. This should settle the issue of "missing diagrams" in our calculation. We, furthermore, demonstrate that our approach allows us to proceed beyond the Golden-rule-type perturbation theory employed by AAG. This explains the difference between our and AAG's results. We also comment on the comparison of our results with the experiments presented by AAG.