粒子运动与混沌
Particle motion and chaos
摘要：
本文考虑粒子落在具有附加势的黑洞中。根据Susskind \cite{Susskind:2018tei}的建议，我们研究了对偶混沌系统中粒子的Rindler动量的增长率，它对应于算子尺寸的增长率。在视界附近的一般分析表明，粒子以规则势下落时的Rindler动量增长率与粒子自由下落时的Rindler动量增长率相同，使混沌束缚饱和。然而，当势为奇异时，生长速率被抑制，使得其低于李雅普诺夫指数。这意味着混沌的抑制可以通过在引力侧增加一个奇异位来实现。我们进一步明确地研究了一个粒子落入超标度破坏时空，以证实一般的分析结果。最后研究了粒子在AdS孤子几何中的下落。它还表现出对林德勒动量增长的抑制。这是由于当引入排斥势或不存在黑洞视界时，粒子被减速，在同向运动的观测者看来，粒子的运动轨迹是类时的，对应于一个弱混沌系统。
英文摘要：
In this note, we consider particle falling in the black hole with an additional potential. Following the proposal by Susskind \cite{Susskind:2018tei}, we study the growth rate of the particle's Rindler momentum, which corresponds to the growth rate of the operator size in the dual chaotic system. A general analysis near the horizon shows that the growth rate of the particle's Rindler momentum of the particle falling with a regular potential is as the same as that of the particle free falling, which saturates the chaos bound. However, when the potential is singular, the growth rate is suppressed such that it is below the Lyapunov exponent. It implies that the chaos suppression may be captured by an additional singular potential in the gravity side. We further explicitly study a particle falling in hyperscaling violating spacetime to confirm the general analysis results. Finally we study the particle falling in AdS soliton geometry. It also exhibits a suppression of the growth of the Rindler momentum. It is attributed to that when the repulsive potential is introduced or the black hole horizon is absent, the particle is slowed down and its trajectory seen by a comoving observer is timelike, which corresponds a weak chaos system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
