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Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
by TianGang Zhou, Pengfei Zhang
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Submission summary
Authors (as registered SciPost users):  Pengfei Zhang 
Submission information  

Preprint Link:  scipost_202303_00026v1 (pdf) 
Date submitted:  20230322 09:00 
Submitted by:  Zhang, Pengfei 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Quench dynamics of fermionic superfluids is an active topic both experimentally and theoretically. Using the BCS theory, such nonequilibrium problems can be reduced to nearly independent spin dynamics only with a timedependent meanfield pairing term. This results in persisting oscillations of the paring strength in certain parameter regimes. In experiments, however, it is observed that the oscillation decays rapidly when the interaction becomes strong, such as in the unitary fermi gas. A theoretical analysis is still absent. In this work, we construct an SYKlike model to analyze the effect of strong interactions in one dimensional BCS system. We utilize the large$N$ approximation and Green's functionbased technique to solve the equilibrium problem and quench dynamics. We find that a strong SYK interaction suppresses the paring order. We further verify that the system quickly thermalizes with SYK interactions for both intrinsic pairing order or proximity effect, which leads to a rapid decay of the strength of the oscillations. The decay rates exhibit different scaling laws against SYK interaction, which can be understood in terms of the Boltzmann equation. Our work makes a first step towards the understanding of attenuating dynamics of strongly interacting fermionic superfluids.
Current status:
Reports on this Submission
Anonymous Report 2 on 2023626 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202303_00026v1, delivered 20230626, doi: 10.21468/SciPost.Report.7403
Strengths
1Noval and Robust Approach: the paper innovatively uses an SYKlike model to address the question of rapidly decaying oscillations in strongly interacting fermionic superfluids, a question that has been challenging to tackle theoretically. The use of largeN approximation combined with Green's functionbased technique ensures a robust and comprehensive approach to solve the equilibrium problem and quench dynamics.
2Relevant to Experiments: The findings from this study are consistent with experimental observations of the rapid decay of oscillations when the interaction in a superfluid becomes strong.
Weaknesses
1Interpretation of Calculations: Some of the calculation results presented in the study lack a thorough physical interpretation. This lack of context can make it challenging for readers to fully grasp the significance of these results or to apply them effectively to their own work. Providing more comprehensive explanations of the implications of the calculations would add depth to the analysis and could offer additional insights into the dynamics of the system under study.
Report
This paper achieves several of these expectations:
1Breakthrough on LongStanding Research Stumbling Block: The rapid decay of pairing strength oscillations in strongly interacting fermionic superfluids has been a longstanding issue in the field. This paper presents a significant breakthrough by providing a theoretical explanation for this phenomenon using an SYKlike model and a Green's functionbased technique.
2Opening New Pathways in Existing Research: By revealing the effects of strong SYK interactions on pairing order and the rate of thermalization, the paper opens new pathways for future research into the dynamics of strongly interacting fermionic superfluids.
3Synergetic Link Between Research Areas: The use of an SYKlike model, originally developed in the context of quantum chaos and black hole physics, to analyze superfluid dynamics represents a novel and synergetic link between different research areas. This innovative application could potentially inspire further crossdisciplinary research.
Therefore, I recommend this paper to publish.
It will be better if the authors consider to give more interpretations of the numerical results. For instance, is the attenuated pairing related to the decreasing quasiparticle weight with the presence of the SYK coupling?
Requested changes
Please check spelling and grammar, e.g. several "pairing" is spelled as "paring"
Anonymous Report 1 on 2023622 (Invited Report)
 Cite as: Anonymous, Report on arXiv:scipost_202303_00026v1, delivered 20230622, doi: 10.21468/SciPost.Report.7387
Strengths
1. Interesting and timely
2. Quite well written and defining fairly precise goals
3. The overall logic is easy to follow and the description of the results is quite clear and useful
Weaknesses
1. Stronger motivation to consider their specific models
2. For nonexpert readers, referencing could be more complete
Report
This manuscript discusses a timely subject and deals with computable models that allow the authors to derive new interesting results that bring the community to a better understanding in the set of open problems discussed in the introduction. For these reasons, my recommendation would be to accept it for publication in this journal after the requests below are taken care of.
Requested changes
1. Despite the motivation given in the introduction, some readers may end up with the impression the main reason the authors considered this model is because it provides a potentially solvable model (in some regime of parameters and energies) where one is probing the effect of some interaction on the degrees of freedom governed by the BCS action. It would benefit the readership of the manuscript if the authors have any stronger reasons to consider these models, in particular, the specific choice appearing in equation (4).
2. It would appear that when they first define the average N should be replaced with $N_s$
3. When applying the large N limit to the nonequilibrium dynamics, the authors mentioned the melodic approximation, i.e. the fact that equation (11) is the leading contribution is an assumption. Could they make this point more precise to help the readers appreciate the dynamical difference between the original equation (11) and the one being discussed in this context ?
4. Readers would benefit if the authors would add some references for : (a) the claim their numerical results qualitatively match similar observations in cold atom experiments at the start of section 3 and (b) the first statement in the first paragraph of section 3.1
5. When discussing the attenuating dynamics, can the authors provide any argument as to why they expect $\delta(0)$ to behave like $1/\Gamma$ ?
Anonymous on 20230529 [id 3692]
This manuscript studies the coupling of a BCS system with an SYKlike model describing random interactions of fermions with different spins in order to gain some understanding and intuition for the attenuating dynamics observed in strongly interacting superconductors or fermionic superfluids.
The manuscript is quite well written and defining fairly precise goals. Once these are established, the overall logic is easy to follow and the description of the results is quite clear and useful.
I have some remarks and questions :  Despite the motivation given in the introduction, some readers may end up with the impression the main reason the authors considered this model is because it provides a potentially solvable model (in some regime of parameters and energies) where one is probing the effect of some interaction on the degrees of freedom governed by the BCS action. It would benefit the readership of the manuscript if the authors have any stronger reasons to consider these models, in particular, the specific choice appearing in equation (4).  It would appear that when they first define the average N should be replaced with $N_s$  When applying the large N limit to the nonequilibrium dynamics, the authors mentioned the melonic approximation, i.e. the fact that equation (11) is the leading contribution is an assumption. Could they make this point more precise to help the readers appreciate the dynamical difference between the original equation (11) and the one being discussed in this context ?  Readers would benefit if the authors would add some references for : (a) the claim their numerical results qualitatively match similar observations in cold atom experiments at the start of section 3 and (b) the first statement in the first paragraph of section 3.1  When discussing the attenuating dynamics, can the authors provide any argument as to why they expect $\delta(0)$ to behave like $1/\Gamma$
I believe the subject of this manuscript is interesting and timely, containing new results related to an interesting open problem. For these reasons, my recommendation would be to accept it for publication in this journal after the above requests are taken care of.