具有动力学混沌的de Sitter空间的Poincaré回归时

Gravity can significantly modify classical and quantum Poincare recurrence theorems

Poincare recurrence theorem states that any finite system will come arbitrary close to its initial state after some very long but finite time. At the statistical level, this by itself does not represent a paradox, but apparently violates the second law of thermodynamics, which may lead to some confusing conclusions for macroscopic systems. However, this statement does not take gravity into account. If two particles with a given center of mass energy come at the distance shorter than the Schwarzschild diameter apart, according to classical gravity they will form a black hole. In the classical c…

Poincare递归与拓扑多样性

Poincare Recurrences and Topological Diversity

有限熵热系统经历庞加莱递归。在场论中，这意味着在有限温度下，类时两点函数将是准周期的。在这篇文章中，我们试图通过研究大量标量场的相关器，利用AdS/CFT对应再现这种行为。我们通过对BTZ时空的所有SL（2，Z）图像求和来评估相关器。我们表明，所有的条款，在此总和后，在某些关键时刻，收到大的修正，并且该结果，即使收敛，是不是准周期的。我们提出了几个参数表明，周期性将是非常难以恢复没有一个确切的求和，并讨论了几个玩具模型，说明这一点。最后，我们考虑信息悖论的后果。

Recurrence Analysis as a tool to study chaotic dynamics of extreme mass ratio inspiral in signal with noise

Recurrence analysis is a well settled method allowing to discern chaos from order, and determinism from noise. We apply this tool to study time series representing geodesic and inspiraling motion of a test particle in a deformed Kerr spacetime, when deterministic chaos and different levels of stochastic noise are present. In particular, we suggest a recurrence-based criterion to reveal whether the time series comes from a deterministic source and find a noise-level threshold of its applicability.

Recurrence plots and chaotic motion around Kerr black hole

We study the motion of charged test particles around a Kerr black hole immersed in the asymptotically uniform magnetic field, concluding that off-equatorial stable orbits are allowed in this system. Being interested in dynamical properties of these astrophysically relevant orbits we employ rather novel approach based on the analysis of recurrences of the system to the vicinity of its previous states. We use recurrence plots (RPs) as a tool to visualize recurrences of the trajectory in the phase space. Construction of RPs is simple and straightforward regardless of the dimension of the phase sp…

Free motion around black holes with discs or rings: between integrability and chaos - II

We continue the study of time-like geodesic dynamics in exact static, axially and reflection symmetric space-times describing the fields of a Schwarzschild black hole surrounded by thin discs or rings. In the previous paper, the rise (and decline) of geodesic chaos with ring/disc mass and position and with test particle energy was revealed on Poincaré sections, on time series of position or velocity and their power spectra, and on time evolution of the orbital `latitudinal action'. In agreement with the KAM theory of nearly integrable dynamical systems and with the results observed in similar …

来自量子混沌的局域庞加莱代数

Local Poincaré Algebra from Quantum Chaos

本文证明在具有模未来/过去 von Neumann 子代数的量子系统中会涌现二维庞加莱代数，并证明模 K 系统总是最大混沌，从而从量子混沌角度解释了近视界局域庞加莱代数的普遍性。