# Are fast scramblers good thermal baths?

### Submission summary

 Authors (as Contributors): Ancel Larzul · Marco Schiro · Steven Thomson
Submission information
Date submitted: 2022-04-19 10:36
Submitted by: Larzul, Ancel
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
Approach: Theoretical

### Abstract

The Sachdev-Ye-Kitaev (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 non-interacting 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 non-interacting 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 system-bath couplings both type of environments give rise to a similar time scale for thermalisation.

###### Current status:
Awaiting resubmission

### Submission & Refereeing History

Submission 2204.06434v1 on 19 April 2022

## Reports on this Submission

### Strengths

1. Very clearly written with well-motivated questions.
2. Detailed numerical calculations supported by semi-analytic calculations.
3. Important insights into the effects of strongly interacting baths, as opposed to non-interacting 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 SYK-related 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 non-thermal steady state of isolated SYK_2 is confusing. It is probably better to use "steady state" instead.

• validity: top
• significance: good
• originality: good
• clarity: top
• formatting: excellent
• grammar: excellent

### Strengths

1. The manuscript addresses the important problem of the thermalization capabilities of a non-interacting 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 system-reservoir couplings is turned on and comment on the suitability of defining an effective temperature in these timescales.

2. Add a comment on the zero-temperature 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)

• validity: top
• significance: high
• originality: high
• clarity: high
• formatting: perfect
• grammar: excellent