SciPost Submission Page
Activity driven transport in harmonic chains
by Ion Santra, Urna Basu
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Urna Basu |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202205_00004v2 (pdf) |
| Date accepted: | 2022-07-27 |
| Date submitted: | 2022-07-08 11:57 |
| Submitted by: | Basu, Urna |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The transport properties of an extended system driven by active reservoirs is an issue of paramount importance, which remains virtually unexplored. Here we address this issue, for the first time, in the context of energy transport between two active reservoirs connected by a chain of harmonic oscillators. The couplings to the active reservoirs, which exert correlated stochastic forces on the boundary oscillators, lead to fascinating behavior of the energy current and kinetic temperature profile even for this linear system. We analytically show that the stationary active current (i) changes non-monotonically as the activity of the reservoirs are changed, leading to a negative differential conductivity (NDC), and (ii) exhibits an unexpected direction reversal at some finite value of the activity drive. The origin of this NDC is traced back to the Lorentzian frequency spectrum of the active reservoirs. We provide another physical insight to the NDC using nonequilibrium linear response formalism for the example of a dichotomous active force. We also show that despite an apparent similarity of the kinetic temperature profile to the thermally driven scenario, no effective thermal picture can be consistently built in general. However, such a picture emerges in the small activity limit, where many of the well-known results are recovered.
Author comments upon resubmission
Dear Editor,
Thank you for forwarding the reports and giving us the opportunity to resubmit our article in Scipost Physics. We also thank both the Referees for their careful reading of the manuscript and the constructive reports. We are glad to see that both the Referees appreciate the scientific merit of our article and recommend publication.
We hereby resubmit a modified version of our article where we have implemented the suggestions of the Referees. Detailed reply to both the reports are appended below. A list of changes is also provided; major modifications are also highlighted in color in the manuscript.
We hope that the current version is suitable for publication in SciPost Physics.
Sincerely, Ion Santra and Urna Basu.
Reply to Anonymous Report 1
We thank the Referee for the positive report and the valuable suggestions, which we have implemented in the revised version.
1 and 2- We have changed 'phonon spectrum' to 'phonon transmission coefficient' in all the relevant places. We also thank the Referee for pointing out the typo, which we have now corrected.
3- We have now added a few sentences in the beginning and at the end of Appendix C, clarifying the nonequilibrium linear response formalism. The response formula tells us that the susceptibility is negative when the <n J> correlation [Eq. (15) in current version] is positive. However, we do not have any clear physical understanding as to when this occurs.
Reply to Anonymous Report 2
We thank the Referee for appreciating our manuscript and for providing a detailed and constructive report. All the changes suggested in the comments (i)--(xii) have been implemented. (xiii) We have added a few sentences in the beginning and at the end of Appendix C clarifying the query.
Minor points: All the typos noted by the Referee and a few additional ones, which we found while rereading, have been corrected.
List of changes
1. We have added 'where j,l=1,N' in Eq. (2).
2. We have referred to Eq. (14) just before Eq. (5).
3. We have given the explicit tri-diagonal form of G(w) in Eq. (9).
4. We have explained the notation \tau_m in the caption of Figure 2 and Sec. 3.1.1.
5. We have consistently changed 'phonon spectrum' to 'phonon transmission coefficient'. In particular, the sentence refereeing to the Landauer like formula has been modified.
6. We have now referred to the saddle point as \tau_1=\tau_N=\bar \tau
7. The sentence refereeing Fig. 5(a) has been modified.
8. We have changed the sentence after Eq. (33) to "The first integral on the second line vanishes as ..."
9. The beginning and end of Appendix C has been modified, clarifying nonequilibrium linear response formalism.
10. We have corrected all the typos pointed out by the Referees and a few additional ones.
All the significant changes have been marked in red.
Published as SciPost Phys. 13, 041 (2022)
Reports on this Submission
Report
In this revised version, the authors have satisfactorily taken into account my comments and made the appropriate modifications. Therefore I can recommend the publication of this manuscript in SciPost. I just noticed a small typo in the paragraph which the authors have added in Appendix C: below Eq. (77), "that the susceptibility" --> "the susceptibility".
Anonymous on 2022-07-18 [id 2666]
I would like to show my appreciation about the preprint "Activity driven transport in harmonic chains". I found the paper well written and the topic is interesting. The search of a negative differential conductivity (NDC) in a different class of problems is relevant and worthwhile.
The authors "address [the transport properties of an extended system driven by active reservoirs] issue, for the first time, in the context of energy transport between two active reservoirs connected by a chain of harmonic oscillators" and show Fig.2 that exhibits a NDC as a function of \tau.
Fig.2 is not an unknown results. The exhistence of a NDC (also called optimal working point, OWP) has been investigated in spin and fermionic chains systems in presence of local boundary dissipators. The problem has been discussed within a different approach, i.e. the Lindblad master equation formalism.
See:
-Fig.1 of "Giuliano Benenti et al 2009 EPL 85 37001";
-Fig.5 of "PHYSICAL REVIEW B 80, 035110 (2009)";
-Fig.18 of "PHYSICAL REVIEW B 103, 115139 (2021)"
I think the authors should briefly discuss the similarity between their model and the above references. This would give a better contextualization of their paper.