AI 中文总结
研究(1 + 1)维ϕ⁸标量场理论中扭结-反扭结碰撞，给出不同真空结构孤子解，通过数值模拟揭示碰撞现象，如特定扇区的湮灭机制、多反弹共振窗口图谱等，提出有效势分类方案预测碰撞结果，突出新动力学特征并建立相关联系。
AI 中文摘要
我们研究了具有多个简并真空的(1 + 1)维ϕ⁸标量场理论中的扭结-反扭结碰撞。给出了以n = p₂/p₁为特征的不同真空结构的显式孤子解。重点关注n = 2和n = 3且有四个不同真空的情况，并在所有拓扑扇区进行了系统数值模拟。发现在(1/2, 1)扇区存在完全湮灭机制，还揭示了跨(-1, -1/2)、(-1, -1/3)和(-1/3, 1/3)扇区的多反弹共振窗口的综合分形图谱。给出了有效势和类薛定谔方程的谱。提出有效势分类方案可为碰撞结果提供预测框架，特别是势类型的突然变化可解释扇区变化和湮灭现象。我们的工作突出了ϕ⁸模型在低阶场论中不存在的新动力学特征，并建立了拓扑结构、振动模式和有效势之间的联系。
英文摘要
We study kink-antikink collisions in a $(1+1)$-dimensional $ϕ^8$ scalar field theory with multiple degenerate vacua. We derive soliton solutions for different vacuum structures labeled by $n=p_2/p_1$, and focus on the cases $n=2$ and $n=3$. We perform numerical simulations in all topological sectors and for both kink-antikink ($K\bar K$) and $\bar K K$ orderings. In the $(-1/2,1/2)$ sector, the kink-antikink pair annihilates for all initial velocities. To the best of our knowledge, this full-velocity annihilation regime has not been reported in $ϕ^8$ kink collisions. We also find fractal multi-bounce windows in the $(-1,-1/2)$, $(-1,-1/3)$, and $(-1/3,1/3)$ sectors. Our main result indicates an effective-potential classification of these collision outcomes. We show that the shape of the effective potential is closely related to the final channel. It determines whether the pair escapes, forms a bion, annihilates, or changes sector. When the solitons pass through each other, the effective potential can change suddenly. This gives a possible mechanism for annihilation and sector change. Our results establish connections among topological structure, spectrum and effective potentials in higher-order scalar field theories.
