论文标题
Gargantuan混乱的引力三体系统及其对普朗克长度的不可逆性
Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length
论文作者
论文摘要
混乱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来表现出来。指数差异推动了时间不可逆性，并增加了系统中的熵。数值后果是，N体问题的整合不可避免地将截断和舍入误差扩大到宏观尺度。迄今为止，恒星动力学系统中的混乱与不可逆性水平之间的定量关系仍然不确定。在这项工作中，我们最初使用准确，精确的N体密码Brutus研究了自由秋季的混乱三体系统，这超出了标准的双精度算术。我们证明，不可逆的解决方案的比例以数值准确性减少为功率定律。这可以源自小初始扰动的放大因子的分布。将此结果应用于由三个具有零总角动量的巨大黑洞组成的系统，我们得出的结论是，此类三元组中多达5％的精度将需要小于普朗克长度的精度，以便产生时间可变的解决方案，从而使它们根本不可预测。
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.
