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_LλL, and is deterministic and non-thermal (T=0T=0). We argue that, if we quantize this system, the quantum fluctuations may imitate thermal fluctuations with temperature $T _L/2 $ 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.
Highlights
Introduction and MotivationPrediction of thermal radiation from a quantum black hole is one of the outstanding achievement in theoretical physics [1, 2]
We review the proposal of Ref. [4] that an emergent quantum thermal nature may appear in dynamical systems that show butterfly effects
Let us consider a classical dynamical system that has a Lyapunov exponent λL1. We assume that this system at classical limit obeys deterministic dynamics and non-thermal. (We are in mind, for example, a driven pendulum motion.) We will argue that, once this system is quantized, the quantum fluctuations may imitate thermal fluctuations with temperature ħh 2π λ in a semi-classical regime
Summary
Prediction of thermal radiation from a quantum black hole is one of the outstanding achievement in theoretical physics [1, 2]. This temperature is proportional to the Plank constant ħh, showing that the temperature arises from a purely quantum effect and it vanishes in classical mechanics (ħh = 0) Such emergent thermal nature in quantum mechanics appears in black holes and in various situations: Unruh effect in accelerated observers, acoustic Hawking radiation in supersonic fluids, moving mirrors and so on [3]. Maldacena, Shenker and Stanford proposed the existence of the bound of chaos [8] They considered quantum many body system at finite temperature and showed that the Lyapunov exponent of the system is generally bounded as λL. If the bound (4) is correct, at least an O(ħh) temperature has to be induced in the system somehow quantum mechanically It sounds like a Hawking radiation, and this prediction motivates us to study non-thermal chaotic systems in the semi-classical regime. Butterfly effect is more essential than chaos in our study as we will see soon
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