Long-range interactions of kinks
Long-range interactions of kinks
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DOI：
10.1103/physrevd.99.016010
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发表时间：
2018-10
影响因子：
5
通讯作者：
I. Christov;Robert J. Decker;A. Demirkaya;V. Gani;P. Kevrekidis;R. V. Radomskiy
中科院分区：
文献类型：
--
作者：
I. Christov;Robert J. Decker;A. Demirkaya;V. Gani;P. Kevrekidis;R. V. Radomskiy
我们给出了高阶场理论中孤立波长程相互作用的计算分析。我们选择的工具是$varphi^8$场理论，尽管我们在$\varphi^{10}$和$\varphi^{12}$模型中探索了类似的问题。特别地，我们讨论了后者的高阶模型与标准的$-varphi^4-$模型之间的根本区别。在建立了模型解逼近其中一个定态的幂函数渐近性态之后，我们证明了这种渐近性在设置多孤子初始条件时需要特别小心。在这样的高阶场理论中，加法或乘法的天真实现会引起非常显著的辐射效应，并最终产生扭结和反扭结之间排斥相互作用的错觉。我们提出并比较了几种如何将初始数据“提取”成合适的数据的方法，并展示了这些方法如何在存在幂函数尾巴(长程相互作用)的情况下捕捉到拓扑孤子之间相互作用的吸引性质。这一进展为系统研究高阶场理论中的孤立波相互作用铺平了道路，并提出了一些关于此类相互作用的潜在实验观测的有趣问题。作为附录，我们用集体坐标的方法分析了算例模型中的扭结-反扭结相互作用。
We present a computational analysis of the long-range interactions of solitary waves in higher-order field theories. Our vehicle of choice is the $\varphi^8$ field theory, although we explore similar issues in example $\varphi^{10}$ and $\varphi^{12}$ models. In particular, we discuss the fundamental differences between the latter higher-order models and the standard $\varphi^4$ model. Upon establishing the power-law asymptotics of the model's solutions' approach towards one of the steady states, we make the case that such asymptotics require particular care in setting up multi-soliton initial conditions. A naive implementation of additive or multiplicative ansatze gives rise to highly pronounced radiation effects and eventually produces the illusion of a repulsive interaction between a kink and an antikink in such higher-order field theories. We propose and compare several methods for how to "distill" the initial data into suitable ansatze, and we show how these approaches capture the attractive nature of interactions between the topological solitons in the presence of power-law tails (long-range interactions). This development paves the way for a systematic examination of solitary wave interactions in higher-order field theories and raises some intriguing questions regarding potential experimental observations of such interactions. As an Appendix, we present an analysis of kink-antikink interactions in the example models via the method of collective coordinates.