论文标题
（1+1）维度之间的拓扑缺陷之间的相互作用
Interactions between topological defects in (1+1) dimensions
论文作者
论文摘要
在本文中，我们研究了二维空间中拓扑缺陷之间的相互作用。这些缺陷称为扭结。它们是标量场理论的解决方案，具有局部能量，而不会失去其形状。为了了解这些模型所表现出的共振现象，我们建立了一个玩具模型，其中扭结模式变成了准模式。这会导致抑制共振窗口，因此，其分形结构丢失了。将高阶多项式视为标量场电位，我们发现具有远距离尾巴的扭结，这会衰减为幂律。我们开发了一种数值方法来正确初始化该系统，并将其应用于包含两侧远距离尾巴的扭结的标量场模型。碰撞后，将扭结 - 安替克对以下的速度歼灭，低于不形成的超相关临界速度。我们还研究了双弦波登模型的摇摆扭结之间的碰撞。当相撞之前扭结已经摇摆时，一次弹跳后出现共振窗口。在论文的后半部分，我们专注于费米恩 - 扭结相互作用。我们研究了费米恩（Fermion）与扭曲的扭结结合时会发生什么。结果是，费米昂以辐射及以恒定的速度从扭结中逃脱。如果初始状态和连续阈值之间的能量差距不大，则会发生这种情况。最后，我们调查了费米昂与背景标量场的相互作用与杂质的相互作用，该杂质保留了Bogomol'nyi-Prasad-Sommerfield（BPS）属性的一半。我们在BPS制度附近发现了绝热的演变，这意味着该系统在每时每刻都处于静态BPS解决方案。
In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In order to understand the resonance phenomenon exhibited by those models, we built a toy model where the kink's vibrational mode turns into a quasinormal mode. This causes the suppression of resonance windows and, consequently, its fractal structure is lost. Considering a higher order polynomial as the scalar field potential, we find kinks with long-range tails, which decay as a power law. We developed a numerical method to correctly initialize this systems and applied it to a scalar field model containing kinks with long-range tails in both sides. After the collision, the kink-antikink pair is annihilated for velocities below an ultra-relativistic critical velocity without bion formation. We also investigated a collision between wobbling kinks of the double sine-Gordon model. When the kinks are already wobbling before colliding, there appears resonance windows with separation after a single bounce. On the second half of the thesis, we focused on fermion-kink interactions. We studied what happens when a fermion binds to a wobbling kink. The result is that the fermion escapes from the kink as radiation and at a constant rate. This occurs if the energy gap between the initial state and the continuum threshold is not too large. Lastly, we investigated the interaction of a fermion with a background scalar field with an impurity that preserves half of the Bogomol'nyi-Prasad-Sommerfield (BPS) property. We found an adiabatic evolution near the BPS regime, which means that the system is at a static BPS solution at every moment.
