A note on late-time tails of spherical nonlinear waves

Linear and nonlinear tails II: exact decay rates in spherical symmetry

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.

具有重尾相互作用的球形Sherrington-Kirkpatrick模型的自由能涨落

Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction

该研究针对无外场的重尾相互作用2自旋球形Sherrington-Kirkpatrick模型，证明自由能存在依赖相互作用矩阵最大特征值位置的尖锐相变，并得到两种区域下极限自由能的阶数与自由能涨落的极限分布。

自由能的严格普遍性二元性：球形铁磁体模型

A Sharp Universality Dichotomy for the Free Energy of Spherical Spin Glasses

研究球形铁磁体模型自由能的严格普遍性二元性，通过不同尾部条件下的变分公式和极值统计分析，揭示了自由能行为的统一分类。

并合黑洞非线性演化中的晚期尾部

Late-time tails in nonlinear evolutions of merging black holes

研究通过SpEC代码揭示并合黑洞非线性数值相对论模拟中的晚期引力波尾部，验证了二体偏心率增强效应，并展示了近单位质量比情况下头对头配置中的尾部特征。

Perturbations of Extremal Kerr Spacetime: Analytic Framework and Late-time Tails

We develop a complete and systematic analytical approach to field perturbations of extremal Kerr spacetime based on the formalism of Mano, Suzuki and Takasugi (MST) for the Teukolsky equation. Analytical expressions for the radial solutions and frequency-domain Green function in terms of infinite series of special functions are presented. As an application, we compute, for the first time, the leading late-time behavior due to the branch point at zero frequency of scalar, gravitational, and electromagnetic field perturbations on and off the event horizon. We also use the MST method to compute t…

线性和非线性晚期时间尾在动态黑洞时空中的表现 via 时间积分

Linear and nonlinear late-time tails on dynamical black hole spacetimes via time integrals

研究通过时间积分方法，揭示动态黑洞时空非线性波动方程的晚期时间尾行为，证明其衰减特性偏离Price定律，适用于更一般的动力学背景。