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

Kink-antikink scattering in nonintegrable field theories like ϕ^{4} theory is still rather poorly understood beyond brute-force numerical calculations, even after several decades of investigation. Recently, however, some progress has been made based on the introduction of certain self-dual background fields in these field theories which imply both the existence of static kink-antikink solutions of the Bogomol'nyi type and the possibility of an adiabatic scattering (moduli space approximation). Here we continue and generalize these investigations by introducing a one-parameter family of models interpolating between the Bogomol'nyi-Prasad-Sommerfield (BPS) model with the self-dual background field and the original ϕ^{4} theory. More concretely, we study kink-antikink scattering in a parameter range between the limit of no static force (BPS limit) and the regime where the static interaction between kink and antikink is small (non-BPS regime). 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 call a thick spectral wall. This phenomenon results from the appearance of a stationary saddle point solution where the acceleration of the solitons owing to the attractive force is compensated by the dynamics of the sufficiently excited mode. Thus, this barrier shows up before the mode crosses the mass threshold.