Many solitonic configurations in field theory have localized bound states in their spectrum of linear perturbations. This opens up the possibility of having long lived excitations of these solitons that could affect their dynamics. We start the study of these effects in the simplest configuration of a domain wall kink solution in the $\lambda \phi^4$ theory in $1+1$ dimensions. We show that this solution has a single bound state and numerically study its slow decay rate in flat space. We then investigate the amplitude of this excitation by simulating a cosmological phase transition that leads to the formation of these kinks in an expanding universe. We find that kinks get formed with a $20\%$ excess of energy with respect to their lowest energy configuration. We also explore the kink solution interacting with a thermal bath and extract the amplitude of the localized excitation as a function of temperature. We note that this amplitude increases with temperature but again the extra energy in the kink never goes over the $20\%$ level. Finally, we argue that this extra energy may have important consequences in the subsequent evolution of defects in numerical simulations.

中文翻译：

---

激发畴壁孤子

场论中的许多孤子配置在其线性扰动谱中具有局部束缚态。这开启了对这些孤子进行长寿命激发的可能性，这些激发可能会影响它们的动力学。我们从 $\lambda\phi^4$ 理论中 $1+1$ 维度的畴壁扭结解的最简单配置开始研究这些效应。我们表明该解具有单一束缚态，并在平坦空间中数值研究其缓慢衰减率。然后，我们通过模拟导致在膨胀的宇宙中形成这些扭结的宇宙相变来研究这种激发的幅度。我们发现，相对于最低能量配置，扭结形成了 $20\%$ 的过剩能量。我们还探索了与热浴相互作用的扭结解决方案，并提取了局部激发的幅度作为温度的函数。我们注意到这个幅度随着温度的增加而增加，但扭结中的额外能量永远不会超过 $20\%$ 的水平。最后，我们认为这种额外的能量可能对数值模拟中随后的缺陷演变产生重要影响。