Phenomena in the kink-antikink Collisions of $ϕ^8$ Theory

Abstract

We investigated kink-antikink collisions in a $(1+1)$-dimensional $ϕ^8$ scalar field theory with multiple degenerate vacua. We presented explicit soliton solutions for different vacuum structures characterized by the ratio $n = p_2/p_1$. We focused on the cases $n=2$ and $n=3$ with four distinct vacua, and performed systematic numerical simulations across all topological sectors. We revealed that there is a complete annihilation regime in the $(1/2,\,1)$ sector, where kink-antikink pairs annihilate for all initial velocities. Up to our knowledge, such phenomenon is first reported in the kink antikink collisions. We revealed a comprehensive fractal cartography of multi-bounce resonance windows across sectors $(-1,\,-1/2)$, $(-1,\,-1/3)$, and $(-1/3,\,1/3)$. Given the kink antikink ($K\bar{K}$, or $\bar{K}K$) ordering, the effective potential and the spectrum of the Schrödinger like equation were presented. By collecting all the effective potential and collision phenomena, we proposed that the effective potential classification scheme provides a predictive framework for collision outcomes including escape, bion formation, sector change, and annihilation. Especially, it is identified that, when soliton pairs pass through each other, the abrupt changes of the potential type could explain both the sector-change and annihilation phenomena. Our work highlight novel dynamical features of the $ϕ^8$ model absent in lower-order field theories, and establish connections between topological structure, vibrational modes, and effective potentials.