Resonance structure in kink-antikink interactions in φ 4 theory

Abstract

We present new numerical and theoretical results concerning kink-antikink collisions in the classical (nonintegrable) φ 4 field model in one-dimensional space. Earlier numerical studies of such collisions revealed that, over a small range of initial velocities, intervals of initial relative velocity for which the kink and antikink capture one another alternate with regions for which the interaction concludes with escape to infinite separation. We describe the results of a new high-precision computer simulation that significantly extends and refines these observations of escape “windows”. We also discuss a simple theoretical mechanism that appears to account for this structure in a natural way. Our picture attributes the alternation phenomenon to a nonlinear resonance between the orbital frequency of the bound kink-antikink pair and the frequency of characteristic small oscillations of the field localized at the moving kink and antikink centers. Our numerical simulation also reveals long-lived small-scale oscillatory behavior in the time dependence of kink and antikink velocity following those collisions that do not lead to capture. We account for this fine structure in terms of the interaction between kink (and antikink) motion and small amplitude “radiation” generated during and after the collision. We discuss possible implications of our results for physical systems.