Analogous Hawking Radiation in Butterfly Effect

TL;DR

This paper suggests that quantum fluctuations in classically chaotic, non-thermal systems can produce phenomena similar to Hawking radiation, linking chaos theory with quantum effects and black hole physics.

Contribution

It introduces a novel idea that quantum effects in butterfly-effect systems can mimic Hawking radiation, providing a new perspective on chaos and quantum gravity.

Findings

Quantum fluctuations can imitate thermal fluctuations with a temperature proportional to Lyapunov exponent.

The proposal offers an intuitive explanation for the chaos bound by Maldacena, Shenker, and Stanford.

Potential connection between butterfly effects and black hole radiation phenomena.

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.