Quasinormal modes in kink excitations and kink-antikink interactions: a toy model

Abstract

We study excitations and collisions of kinks in a scalar field theory where the potential has two minima with $Z_2$ symmetry. The field potential is designed to create a square well potential in the stability equation of the kink excitations. The stability equation is analogous to the Schrödinger equation, and therefore we use quantum mechanics techniques to study the system. We modify the square well potential continuously, which allows the excitation to tunnel and consequently turns the normal modes of the kink into quasinormal modes. We study the effect of this transition, leading to energy leak, on isolated kink excitations. Finally, we investigate kink-antikink collisions and the resulting scaling and fractal structure of the resonance windows considering both normal and quasinormal modes and compare the results.

23 pages, 11 figures

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• Semi-compactness and multiple oscillating pulses in kink scattering
• Kink-antikink collision in the supersymmetric ${\varphi }^4$ model
• Fermions on wobbling kinks: normal versus quasinormal modes
• Emergence of oscillons in kink-impurity interactions
• A new model with solitary waves: solution, stability and quasinormal modes