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Register a new userResonant kink-antikink scattering through quasinormal modes
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Romanczukiewicz Tomasz Ph.D.
Publication date
2017
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English
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We investigate the role that quasinormal modes can play in kink-antikink collisions, via an example based on a perturbation of the $phi^4$ model. We find that narrow quasinormal modes can store energy during collision processes and return it back to the translational degrees of freedom. Quasinormal modes also decay, which leads to energy leakage, causing a closing of resonance windows and an increase of the critical velocity. We observe similar phenomena in an effective model, a small modification of the collective-coordinate approach to the $phi^4$ model.
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Kink-antikink scattering in the $phi^4$ model is investigated in the limit when the static inter-soliton force vanishes. We observe the formation of spectral walls and, further, identify a new phenomenon, the vacuum wall, whose existence gives rise to a bouncing structure for the annihilating solitons. Furthermore, we discover higher order spectral walls, i.e., spectral walls which form when higher harmonics enter the continuous spectrum. These higher order spectral walls not only deform the soliton trajectories, they also can be observed easily as very intense radiation bursts.
We show that in some kink-antikink (KAK) collisions sphalerons, i.e., unstable static solutions - rather than the asymptotic free soliton states - can be the source of the internal degrees of freedom (normal modes) which trigger the resonance phenomenon responsible for the fractal structure in the final state formation.
Recent studies have emphasized the important role that a shape deformability of scalar-field models pertaining to the same class with the standard $phi^4$ field, can play in controlling the production of a specific type of breathing bound states so-called oscillons. In the context of cosmology, the built-in mechanism of oscillons suggests that they can affect the standard picture of scalar ultra-light dark matter. In the present work kink scatterings are investigated in a parametrized model of bistable system admitting the classical $phi^4$ field as an asymptotic limit, with focus on the formation of long-lived low-amplitude almost harmonic oscillations of the scalar field around a vacuum. The parametrized model is characterized by a double-well potential with a shape-deformation parameter that changes only the steepness of the potential walls, and hence the flatness of the hump of the potential barrier, leaving unaffected the two degenerate minima and the barrier height. It is found that the variation of the deformability parameter promotes several additional vibrational modes in the kink-phonon scattering potential, leading to suppression of the two-bounce windows in kink-antikink scatterings and the production of oscillons. Numerical results suggest that the anharmonicity of the potential barrier, characterized by a flat barrier hump, is the main determinant factor for the production of oscillons in double-well systems.
We study kink-antikink scattering in a one-parameter variant of the $phi^4$ theory where the model parameter controls the static intersoliton force. We interpolate between the limit of no static force (BPS limit) and the regime where the static interaction is small (non-BPS). This allows us to study the impact of the strength of the intersoliton static force on the soliton dynamics. In particular, we analyze how the transition of a bound mode through the mass threshold affects the soliton dynamics in a generic process, i.e., when a static intersoliton force shows up. We show that the thin, precisely localized spectral wall which forms in the limit of no static force, broadens in a well-defined manner when a static force is included, giving rise to what we will call a thick spectral wall. This phenomenon just requires that a discrete mode crosses into the continuum at some intermediate stage of the dynamics and, therefore, should be observable in many soliton-antisoliton collisions.
The fractal velocity pattern in symmetric kink-antikink collisions in $phi^4$ theory is shown to emerge from a dynamical model with two effective moduli, the kink-antikink separation and the internal shape mode amplitude. The shape mode usefully approximates Lorentz contractions of the kink and antikink, and the previously problematic null-vector in the shape mode amplitude at zero separation is regularized.
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