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Noiseinduced transport in the AubryAndréHarper model
by Devendra Singh Bhakuni, Talía L. M. Lezama and Yevgeny Bar Lev
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Authors (as registered SciPost users):  Yevgeny Bar Lev · Devendra Singh Bhakuni · Talía L. M. Lezama 
Submission information  

Preprint Link:  scipost_202307_00026v2 (pdf) 
Date submitted:  20231106 19:57 
Submitted by:  Bhakuni, Devendra Singh 
Submitted to:  SciPost Physics 
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Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We study quantum transport in a quasiperiodic AubryAndréHarper (AAH) model induced by the coupling of the system to a Markovian heat bath. We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase. Increasing the number of coupled sites at the central region introduces a transient diffusive regime, which crosses over to logarithmic transport in the localized phase and in the delocalized regime to ballistic transport. On the other hand, when the heat bath is coupled to equally spaced sites of the system, we observe a crossover from ballistic and logarithmic transport to diffusion in the delocalized and localized regimes, respectively. We propose a classical master equation, which in the localized phase, captures our numerical observations for both coupling configurations on a qualitative level and for some parameters, even on a quantitative level. Using the classical picture, we show that the crossover to diffusion occurs at a time that increases exponentially with the spacing between the coupled sites, and the resulting diffusion constant decreases exponentially with the spacing.
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Reports on this Submission
Report #2 by Anonymous (Referee 4) on 20231112 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202307_00026v2, delivered 20231112, doi: 10.21468/SciPost.Report.8096
Report
The Authors have improved the Introduction and provided a more clear motivation for their study. I still find the choice of bath coupling schemes rather artificial and therefore of narrow interest.
The results on entanglement entropy could have been expanded, instead the Authors decided to move them to the Appendix.
More importantly, I am still not fully satisfied with the Authors discussion of their theoretical approach: the single particle propagator above Eq. (7) is not defined. How are they solving the dynamics?What is the filling of the system? In section II they mention N particles in L sites, but I could not find the value of N. Are the Authors considering the one particle sector, N=1?
Finally, it is not obvious to me that in presence of a nonuniform bath coupling (for example scheme a) the stationary state is infinite temperature, as the Authors assume in this work. I could imagine some interesting crossover with \ell (the size of the region coupled to the bath), where the rest of the system act as another bath leading to a nonequilibrium steady state, with effective temperature ultimately going to infinity with \ell? The Authors should at least comment on this point.
Based on these comments I conclude the paper does not meet the criteria for SciPost Physics. If the Authors address the points above (clarification of their method and of the validity of the infinite temperature state) the manuscript can be accepted in SciPost Physics Core.
Report #1 by Anonymous (Referee 3) on 2023118 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202307_00026v2, delivered 20231108, doi: 10.21468/SciPost.Report.8076
Report
Yes, the authors have made appropriate improvements. Except:
The last sentence of the caption to Fig 6 says: "The dashed blue line corresponds to the theoretical prediction, with no fitting parameters." But there is no dashed blue line in the figure. And I could not find a theoretical prediction without fitting parameters for D anywhere in the text. So this needs to be fixed in multiple ways. Make it very clear what theoretical prediction you are showing, and why (how) such a prediction can be made without any fitting parameters (and, if I understand, end up off by an order of magnitude or so). My guess is that there really is not any such prediction, just an expected scaling with an unknown multiplicative factor (which thus ends up as a fitting parameter).
Author: Yevgeny Bar Lev on 20231128 [id 4152]
(in reply to Report 1 on 20231108)
**The referee writes:**
>The last sentence of the caption to Fig 6 says: "The dashed blue line corresponds to the theoretical prediction, with no fitting parameters." But there is no dashed blue line in the figure. And I could not find a theoretical prediction without fitting parameters for D anywhere in the text. So this needs to be fixed in multiple ways. Make it very clear what theoretical prediction you are showing, and why (how) such a prediction can be made without any fitting parameters (and, if I understand, end up off by an order of magnitude or so). My guess is that there really is not any such prediction, just an expected scaling with an unknown multiplicative factor (which thus ends up as a fitting parameter)
**Our response:**
We thank the referee for finding the problem in the caption. We have fixed it and added the explicit expression for the theoretical prediction. The referee is correct that the theoretical prediction is based on the analysis of the relevant time and length scales and, therefore, cannot be expected to match the numerical value of D. Nevertheless, it does capture nicely its dependence on $\lambda$, up to a numerical prefactor.
Author: Yevgeny Bar Lev on 20231128 [id 4151]
(in reply to Report 2 on 20231112)The referee writes:
Our response: In our previous response, we have explained that the theoretical framework is general and applies to all possible couplings. Therefore, we are surprised by the referee's comment that our results are narrowly interesting. Since we can only study specific choices numerically, we have decided to focus on the deterministic spacing of the couplings, which is more appropriate to the AubryAndre model and more experimentally relevant. Appendix B includes results for coupling to random sites.
The referee writes:
Our response: We accepted the comment in the initial report that the entanglement part is decoupled from the rest of the story. We moved this part to the Appendix to make the story more focused.
The referee writes:
Our response: We thank the referee for pointing this out. We have added a definition of the singleparticle propagator, which follows directly from Eq. (4). The correlation function is calculated in the infinite temperature state, which averages over all particle sectors. We have added a clarifying comment above Eq (7) and removed N from the leading sentence of Sec II, which is not used anyway. We also added the average over noise trajectories (denoted by an overbar) which was missing in the definition of the root mean squared displacement and in the legend of the figure of the entanglement entropy in the appendix, which is of course averaged over noise trajectories as well.
The referee writes:
Our response: Just above Eq (6), we write "It is easy to check that irrespective of H the RHS of Eq. (2) vanishes for Hermitian Lindblad jump operators and $\hat{\rho}\propto\mathbb{I}$", where Eq (2) is the Lindblad equation. Since this can be checked by a simple substitution, we decided not to add an explicit derivation in the text. Therefore, if the stationary state is unique, it must be the infinite temperature state, even when the coupling is only to one site.