论文标题
扭结 - 安提克克的互动力和绑定状态在双旋转$ ϕ^4 $型号中
Kink-Antikink Interaction Forces and Bound States in a Biharmonic $ϕ^4$ Model
论文作者
论文摘要
我们考虑唯一的相互作用在研究良好的$ ϕ^4 $ klein-gordon理论的双旋转梁模型类似物中。具体而言，我们计算出良好的分离扭结和抗京键之间的力。知道它们的加速度是分离的函数，我们可以使用简单的颂歌来确定它们的运动。这种渐近分析与数值计算之间有很好的一致性。重要的是，我们发现该力具有指数的振荡行为（与Klein-Gordon案例中单调有吸引力的相互作用不同）。与力量的零相对应，我们预测了一组无限的野外理论平衡的存在，即扭结 - 坦克克结合状态。我们在PDE级别上确认其中的前几个，并验证其预期的稳定性或不稳定。我们还探讨了这种相互作用力在扭结与反对动态的反京族之间的碰撞中的含义。
We consider the interaction of solitons in a biharmonic, beam model analogue of the well-studied $ϕ^4$ Klein-Gordon theory. Specifically, we calculate the force between a well separated kink and antikink. Knowing their accelerations as a function of separation, we can determine their motion using a simple ODE. There is good agreement between this asymptotic analysis and numerical computation. Importantly, we find the force has an exponentially-decaying oscillatory behaviour (unlike the monotonically attractive interaction in the Klein-Gordon case). Corresponding to the zeros of the force, we predict the existence of an infinite set of field theory equilibria, i.e., kink-antikink bound states. We confirm the first few of these at the PDE level, and verify their anticipated stability or instability. We also explore the implications of this interaction force in the collision between a kink and an oppositely moving antikink.
