Kink-antikink collisions in a weakly interacting ϕ^{4} model

Area of Science:

• * Theoretical and Mathematical Physics
• * Quantum Field Theory
• * Soliton Dynamics

Background:

• * Kink-antikink scattering in nonintegrable field theories, such as \( \phi^4 \) theory, remains challenging to analyze beyond numerical simulations.
• * Recent advancements involve self-dual background fields, enabling static kink-antikink solutions (Bogomol'nyi type) and adiabatic scattering approximations (moduli space approximation).

Purpose of the Study:

• * To generalize investigations of kink-antikink scattering by introducing a one-parameter family of models.
• * To study the impact of static inter-soliton forces on soliton dynamics.
• * To analyze the transition of bound modes through the mass threshold in kink-antikink scattering.

Main Methods:

• * Introduction of a one-parameter model family interpolating between the Bogomol'nyi-Prasad-Sommerfield (BPS) model and the \( \phi^4 \) theory.
• * Examination of kink-antikink scattering within a parameter range from the BPS limit (no static force) to the non-BPS regime (small static force).
• * Analysis of the spectral wall's behavior and the emergence of a stationary saddle point solution.

Main Results:

• * Demonstrated the effect of static inter-soliton force strength on soliton dynamics.
• * Showed that a thin spectral wall in the BPS limit broadens into a "thick spectral wall" when static forces are present.
• * Identified a stationary saddle point solution where soliton acceleration is balanced by excited mode dynamics.

Conclusions:

• * The study provides a framework for understanding kink-antikink scattering in a more general setting.
• * The formation of a "thick spectral wall" is a key phenomenon resulting from the interplay between static forces and soliton modes.
• * This spectral wall appears before the bound mode crosses the mass threshold, offering new insights into scattering dynamics.