# Analogous Hawking Radiation in Butterfly Effect

### Submission summary

 As Contributors: Takeshi Morita Preprint link: scipost_202010_00029v1 Date submitted: 2020-10-31 09:31 Submitted by: Morita, Takeshi Submitted to: SciPost Physics Proceedings Proceedings issue: 4th International Conference on Holography, String Theory and Discrete Approach in Hanoi Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We propose that Hawking radiation-like phenomena may be observed in systems that show butterfly effects. Suppose that a classical dynamical system has a Lyapunov exponent $\lambda_L$, and is deterministic and non-thermal ($T=0$). We argue that, if we quantize this system, the quantum fluctuations may imitate thermal fluctuations with temperature $T \sim \hbar \lambda_L/2 \pi$ in a semi-classical regime, and it may cause analogous Hawking radiation. We also discuss that our proposal may provide an intuitive explanation of the existence of the bound of chaos proposed by Maldacena, Shenker and Stanford.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission scipost_202010_00029v2 on 16 December 2020

Submission scipost_202010_00029v1 on 31 October 2020

## Reports on this Submission

### Anonymous Report 1 on 2020-12-13 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202010_00029v1, delivered 2020-12-13, doi: 10.21468/SciPost.Report.2286

### Strengths

1-) the paper is well written and presents its main ideas clearly;

2-) the content of the paper is original and its main proposal is well-motivated via a few pedagogical examples;

3-) the paper helps to better understand the origin of the so-called bound on chaos, which is important in the context of black holes physics, many-body quantum chaos, condensed matter theory, etc.

### Weaknesses

1-) In my opinion, the paper is already very good, but it could be even better if the author provides a more detailed comparison with previous results in the literature. In particular, I think the paper would greatly benefit from a more detailed comparison with the results of reference [9], by J. Kurchan.

### Report

In the paper "Analogous Hawking Radiation in Butterfly Effect", Takeshi Morita proposes that in non-thermal systems that show sensitive dependence on initial conditions, quantum mechanics effects lead to the appearance of an effective temperature.

The author argues that the bound on chaos, $\lambda_L \leq \frac{2 \pi T}{\hbar}$, might be seen as a lower bound to the system's temperature: $T \geq \frac{\hbar \lambda_L}{2 \pi}$. In particular, the effective temperature introduced by quantum effects, $T_\text{eff} \sim \frac{\hbar \lambda_L}{2 \pi}$, defines a thermal scale below which quantum fluctuations overcome the thermal ones, and the thermal equilibrium may be disturbed. This provides a nice way to understand the chaos bound proposed by Maldacena, Shenker, and Stanford.

In my opinion, the paper is well written and presents original content. Therefore, I recommend the paper for publication after one minor clarification has been addressed.

### Requested changes

1-)
I think the paper would greatly benefit if the author includes a more detailed comparison with previous results in the literature, in particular with reference [9], by J. Kurchan.
In [9], J. Kurchan explains the bound on chaos in a simple way. He defines a Lyapunov length scale, $\ell_0$, and argues that the bound on chaos appears when $\ell_0$ is comparable to the de Broglie length scale $\ell_\text{dB}$. Since, $\ell_0 \sim T^{1/2}$ and $\ell_\text{dB} \sim T^{-1/2}$, J. Kurchan's results seem to be consistent with the results obtained by Takeshi Morita, because for very low temperatures the de Broglie length scale becomes bigger than the Lyapunov length scale. I think the author could add a paragraph comparing his results with the ones in reference [9].

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

### Author:  Takeshi Morita  on 2020-12-16  [id 1083]

(in reply to Report 1 on 2020-12-13)
Category: