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Are fast scramblers good thermal baths?
by Ancel Larzul, Steven J. Thomson, M. SchirĂ²
Submission summary
Authors (as registered SciPost users):  Ancel Larzul · Marco SchirĂ² · Steven Thomson 
Submission information  

Preprint Link:  https://arxiv.org/abs/2204.06434v1 (pdf) 
Date submitted:  20220419 10:36 
Submitted by:  Larzul, Ancel 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
The SachdevYeKitaev (SYK$_{4}$) model has attracted attention for its fast scrambling properties and its thermalization rate that is set only by the temperature. In this work we ask the question of whether the SYK$_{4}$ model is also a good thermal bath, in the sense that it allows a system coupled to it to thermalize. We address this question by considering the dynamics of a system of $N$ random noninteracting Majorana fermions coupled to an SYK$_{4}$ bath with $M$ Majorana fermions that we solve with Keldysh techniques in the limit of $M\gg N\gg 1$. We compare this nonequilibrium setting with a conventional bath made of free noninteracting degrees of freedom with a continous spectrum. We show that the SYK$_{4}$ bath is more efficient in thermalising the system at weak coupling, due to its enhanced density of states at low frequency, while at strong systembath couplings both type of environments give rise to a similar time scale for thermalisation.
Current status:
Reports on this Submission
Strengths
1. Very clearly written with wellmotivated questions.
2. Detailed numerical calculations supported by semianalytic calculations.
3. Important insights into the effects of strongly interacting baths, as opposed to noninteracting baths usually used for open quantum systems, on the thermalization of a system that does not otherwise thermalize.
Weaknesses
1. No discussions on how the insights obtained using the SYK model as a bath will be useful for more realistic baths that can be realized in actual experiments.
2. The manuscript certainly satisfies several of the general acceptance criteria listed by SciPost, but it is not clear which of the expectations i.e. detail a groundbreaking theoretical discovery, present a breakthrough .., open a new pathway .., etc., the manuscript fulfills.
Report
I will recommend publications if the authors could strengthen the introduction and more clearly state how their work goes much beyond many previous works on thermalization in SYK and related models. The authors should also add some discussions on how the work can be relevant to the more general situations, beyond only SYKrelated physics, e.g. for experimentally realizable systems coupled to more realistic baths.
Requested changes
1. I think Eq.(4) has a typo; \Sigma^R(\mathcal{T},\omega) in the last term should be replaced by \Sigma^A(\mathcal{T},\omega).
2. The final temperature combined system is T_B, but in Section 5, the authors suddenly use \beta_f. Also \mathcal{T}_0 is used for the initial time in this section without properly defining it.
3. The word "equilibrate" to describe the nonthermal steady state of isolated SYK_2 is confusing. It is probably better to use "steady state" instead.
Strengths
1. The manuscript addresses the important problem of the thermalization capabilities of a noninteracting and strongly interacting baths.
2. It contains a number of analytical findings carefully supported by numerical results.
Report
I deem the paper suited for publication in SciPost Physics after some minor issues and clarifications are addressed.
Requested changes
1. Show the adequacy of the fits to Eq.(37) of the distribution function during the times immediately after the systemreservoir couplings is turned on and comment on the suitability of defining an effective temperature in these timescales.
2. Add a comment on the zerotemperature limit.
3. Comment on the possibility of the thermalization rate \lambda being obtained within linear response theory around the equilibrium state.
4. Correct a typo in Eq.(44)