Nurminen, Niilo Waltteri
(Helsingin yliopisto, 2021)
Phase transitions in the early Universe and in condensed matter physics are active fields of research. During these transitions, objects such as topological solitons and defects are produced by the breaking of symmetry. Studying such objects more thoroughly could shed light on some of the modern problems in cosmology such as baryogenesis and explain many aspects in materials research.
One example of such topological solitons are the (1+1) dimensional kinks and their respective higher dimensional domain walls. The dynamics of kink collisions are complicated and very sensitive to initial conditions. Making accurate predictions within such a system has proven to be difficult, and research has been conducted since the 70s. Especially difficult is predicting the location of resonance windows and giving a proper theoretical explanation for such a structure. Deeper understanding of these objects is interesting in its own right but can also bring insight in predicting their possibly generated cosmological signatures.
In this thesis we have summarized the common field theoretic tools and methods for the analytic treatment of kinks. Homotopy theory and its applications are also covered in the context of classifying topological solitons and defects. We present our numerical simulation scheme and results on kink-antikink and kink-impurity collisions in the $\phi^4$ model. Kink-antikink pair production from a wobbling kink is also studied, in which case we found that the separation velocity of the produced kink-antikink pair is directly correlated with the excitation amplitude of the wobbling kink. Direct annihilation of the produced pair was also observed.
We modify the $\phi^4$ model by adding a small linear term $\delta \phi^3$, which modifies the kinks into accelerating bubble walls. The collision dynamics and pair production of these objects are explored with the same simulation methods. We observe multiple new effects in kink-antikink collisions, such as potentially perpetual bouncing and faster bion formation in comparison to the $\phi^4$ model. We also showed that the $\delta$ term defines the preferred vacuum by inevitably annihilating any kink-antikink pair. During pair production we noticed a momentum transfer between the produced bion and the original kink and that direct annihilation seems unlikely in such processes. For wobbling kink - impurity collisions we found an asymmetric spectral wall. Future research prospects and potential expansions for our analysis are also discussed.