Kink-antikink collisions in piecewise potentials — stitched together from different functional forms, dubbed “Frankensteinian” — act as particle-production factories with built-in thresholds.
Lower the field threshold and the collision's character changes. Not gradually. A phase-transition-like switch flips across a large range of initial velocities simultaneously: collisions that previously disintegrated into radiation start producing oscillons — long-lived localized oscillations that persist far longer than the collision event.
The transition is sharp. On one side of the threshold, the collision debris disperses. On the other, it condenses into bound states. And this happens not for a single carefully chosen velocity but across whole swaths of the velocity space at once.
The kink collision becomes a tunable matter-creation machine. Adjust one parameter (the field threshold where potential pieces join), and the entire output regime changes character.
This is the hallmark of a genuine phase transition rather than a crossover: the qualitative change is sudden, affects a macroscopic region of parameter space, and doesn't require fine-tuning to observe. The collision knows what to produce before the kinks meet — the potential shape has already decided.