巨混沌引力三体系统及其普朗克长度不可逆性
Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length
摘要：
混沌存在于大多数恒星动力学系统中，并通过小扰动的指数增长表现出来。指数发散驱动时间不可逆性并增加系统中的熵。数值结果是N体问题的积分将截断和舍入误差放大到宏观尺度。然而，恒星动力学系统中的混沌与不可逆性之间的定量关系仍然没有确定。在这项工作中，我们研究混沌三体系统的自由降落最初使用准确和精确的N体代码布鲁特斯，这超出了标准的双精度算法。我们证明了不可逆解的分数随着数值精度的幂律而减少。这可以从小的初始扰动的放大因子的分布导出。将这个结果应用到由三个角动量为零的大质量黑洞组成的系统中，我们得出结论，高达5%的三重黑洞需要小于普朗克长度的精度才能产生时间可逆的解，从而使它们从根本上不可预测。
英文摘要：
Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical consequence is that integrations of the N-body problem unavoidably magnify truncation and rounding errors to macroscopic scales. Hitherto, a quantitative relation between chaos in stellar dynamical systems and the level of irreversibility remained undetermined. In this work we study chaotic three-body systems in free fall initially using the accurate and precise N-body code Brutus, which goes beyond standard double-precision arithmetic. We demonstrate that the fraction of irreversible solutions decreases as a power law with numerical accuracy. This can be derived from the distribution of amplification factors of small initial perturbations. Applying this result to systems consisting of three massive black holes with zero total angular momentum, we conclude that up to five percent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable.
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