标题： 因果钻石的共形量子力学：量子不稳定性与半经典近似 显示英文标题

标题： Conformal quantum mechanics of causal diamonds: Quantum instability and semiclassical approximation

摘要： 因果光锥已知具有可以通过配备能量缩放探测器的有限寿命观察者探测的热行为。 这种热性可以归因于因果光锥内观察者的演化，该演化由共形量子力学（CQM）对称性生成元之一——非紧致双曲算子$S$所支配。 在本文中，我们表明$S$的无界性使其具有量子不稳定性，这是类似于倒置谐波振荡势所表现出的类似性质的一种推广。 我们的分析是半经典的，包括对$S$的经典动力学及其对偶算子$R$的详细相空间研究，以及一个一般的半经典框架，该框架产生基本的不稳定性与热性特性，在理论的量子行为中起着关键作用。 对于一个有限寿命的观察者$\mathcal{T}$，检测到的温度$T_D = 2 \hbar/(\pi \mathcal{T})$与李雅普诺夫指数$\lambda_L = \pi T_D/\hbar$相关，该指数是信息杂乱率的上限饱和值的一半。 显示英文摘要

摘要： Causal diamonds are known to have thermal behavior that can be probed by finite-lifetime observers equipped with energy-scaled detectors. This thermality can be attributed to the time evolution of observers within the causal diamond, governed by one of the conformal quantum mechanics (CQM) symmetry generators: the noncompact hyperbolic operator $S$. In this paper, we show that the unbounded nature of $S$ endows it with a quantum instability, which is a generalization of a similar property exhibited by the inverted harmonic oscillator potential. Our analysis is semiclassical, including a detailed phase-space study of the classical dynamics of $S$ and its dual operator $R$, and a general semiclassical framework yielding basic instability and thermality properties that play a crucial role in the quantum behavior of the theory. For an observer with a finite lifetime $\mathcal{T}$, the detected temperature $T_D = 2 \hbar/(\pi \mathcal{T})$ is associated with a Lyapunov exponent $\lambda_L = \pi T_D/\hbar$, which is half the upper saturation bound of the information scrambling rate.