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On scrambling, tomperature and superdiffusion in de Sitter space
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abstract
This paper investigates basic properties of the de Sitter static patch using simple two-point functions in the probe approximation. We find that de Sitter equilibrates in a superdiffusive manner, unlike most physical systems which equilibrate diffusively. We also examine the scrambling time. In de Sitter, the two-point functions of free fields do not decay for sometime because quanta can reflect off the pole of the static patch. This suggests a minimum scrambling time of the order $\log(1/G_N)$, even for perturbations introduced on the stretched horizon, indicating fast scrambling inside de Sitter static patch. We also discuss the interplay between thermodynamic temperature and inverse correlation time, sometimes called "tomperature".
Forward citations
Cited by 2 Pith papers
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Out-of-time-ordered Correlators in de Sitter Revisited
The de Sitter OTOC grows at the maximal Lyapunov rate 2π/β at tree level and at twice that rate in a massive-graviton-regulated double-scaling limit, with the growth traced to large diffeomorphisms in the graviton propagator.
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On the late time behavior of thermal two point function in curved space-time
For thermal Bose fields in static de Sitter or a planar BTZ black hole, the late-time correlation decay switches from temperature-limited to quasinormal-mode-limited at a critical temperature Tc.
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