Resonance Structure in Kink-Antikink Interactions

Abstract

Topological defects, which emerge as solutions to field theories, are intimately linked to phase transition phenomena. A fundamental example of such defects is the kink (and its counterpart, antikink) in (1 + 1) dimensional systems, representing static solutions. When these defects interact, they exhibit a wide variety of behaviors, including the formation of fractal structures. In well-known models such as the λφ4 theory, interactions involve localized vibrational modes, which are confined to individual elements of the system. In contrast, the φ6 model features delocalized modes extending across the kink-antikink pair. In the latter, the frequencies of the delocalized modes depend on the pair’s separation. This thesis introduces a toy model based on a piecewise potential, V (φ) ∼ φ2, which facilitates a detailed exploration of the phenomenon known as the energy exchange mechanism. By adjusting two free parameters, the model allows for systematically studying the impact of adding localized and delocalized frequencies and their interplay with the kinetic energy of the kinks.