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تسجيل مستخدم جديدCollective coordinate model of kink-antikink collisions in $phi^4$ theory
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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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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 inter
action 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.
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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 phenome
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