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.
Highlights
In field equations in (1 + 1) dimensions there are solitary wave solutions called kinks which interpolate between neighboring minima of the potential
The role of the normal mode excitations in kink–antikink collision has been already known since the work of Sugiyama [23], where the author could estimate the critical velocity of the φ4 using a collective coordinate approximation
The role of the normal modes excitation in the resonance windows was first explained in a seminal paper by Campbell et al [22] where they showed that there is an interplay between the translational mode of the kink and the vibrational or “shape” mode in a resonant energy exchange mechanism
Summary
In field equations in (1 + 1) dimensions there are solitary wave solutions called kinks which interpolate between neighboring minima of the potential. We are interested in investigating how isolated kink excitations and collisions of a kink and an antikink are affected as the normal mode turns gradually into a QNM, using a toy model For this to happen we look at the small fluctuations around the kink solutions and the corresponding Schrödinger-like stability equations. The authors studied the kink–antikink interactions when the normal modes of the latter model ( = 0) turn into the QNMs of the former one ( = 0) This “volcano shaped” linear stability potentials appear in other models such as vacuumless systems [69] and kinks with power-law asymptotics [66].
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