Resonance structures in kink-antikink scattering in a quantum vacuum

We investigate kink-antikink scattering in the $\lambda {\phi }^4$ model in the presence of an additional scalar field, $\psi$, that is in its quantum vacuum and interacts with $\phi$ via a $\xi {\phi }^2{\psi }^2$ term where $\xi$ is the coupling. The final state of such a scattering is either a bound state with eventual annihilation or a reflection of the kink-antikink pair. Without the $\psi$ field, the outcome is known to depend fractally on the initial velocity of the kink-antikink pair. In the quantum vacuum of the $\psi$ field, the fractal dependence gets modified and disappears above a critical interaction strength, $\xi \approx 0.1$.