Conformal quantum mechanics of causal diamonds: Quantum instability and semiclassical approximation
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| author | Camblong, H. E. Chakraborty, A. Lopez-Duque, P. Ordóñez, C. |
| author_facet | Camblong, H. E. Chakraborty, A. Lopez-Duque, P. Ordóñez, C. |
| contents | 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
$T_D = 2 \hbar/(π\mathcal{T})$ is associated with a Lyapunov exponent $λ_L = πT_D/\hbar$, which is half the upper saturation bound of the information scrambling rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18191 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal quantum mechanics of causal diamonds: Quantum instability and semiclassical approximation Camblong, H. E. Chakraborty, A. Lopez-Duque, P. Ordóñez, C. Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 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 $T_D = 2 \hbar/(π\mathcal{T})$ is associated with a Lyapunov exponent $λ_L = πT_D/\hbar$, which is half the upper saturation bound of the information scrambling rate. |
| title | Conformal quantum mechanics of causal diamonds: Quantum instability and semiclassical approximation |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.18191 |