PhD thesis defense of Paweł Tatrocki

Numerical studies of kink configurations of the φ⁴ model in systems that explicitly break down translational invariance

The dissertation discusses the method of collective coordinates, ie the method of reduction of the dynamics of the system with infinitely many degrees of freedom to the dynamics of the system with several degrees of freedom. It has been shown that the collective coordinate method is an appropriate tool for studying both slow and fast-moving kinks. It has been shown that until the bound states are not formed, this method leads to correct results. The thesis describes the process of formation of kinks in spatially non-homogeneous systems. In the framework of the field model, the process of transformation of a stationary kink into a deformed kink trapped by an admixture was also examined. The thesis states that in addition to the commonly known radiation processes, the reduction of the kinetic energy of the kink occurs due to the confinement of part of the kinetic energy by the heterogeneity in the form of gradient field energy. Both processes are of great importance for the evolution of the kink system, because they lead to the reduction of kink speed and to the confinement of a substantial part of these objects by impurities – this process terminate the kink-antikink annihilation. The work discusses the creation of kink type structures during a non-uniform spatial phase transition. In spatially uniform systems, in the case when the speed of the phase front is smaller than the velocity of the decay of the false vacuum, behind the front of the transition, defects are not formed. The work shows that there are three possible scenarios in spatial heterogeneous systems. In two scenarios defects are created, and only in the last scenario defects are not formed.