Oscillons and bubbles in $Q$-ball dynamics

Abstract: We show that, in the thin-wall regime, $Q$-ball--anti-$Q$-ball collisions reveal chaotic behaviour. This is explained by the resonant energy transfer mechanism triggered by the internal modes hosted by the $Q$-balls and by the existence of {\it ephemeral} states, that is unstable, sometimes even short-lived, field configurations that appear as intermediate states. The most important examples of such states are the {\it bubble} of the false broken vacuum, which as intermediate states govern the $QQ^*$ annihilation, and the {\it charged oscillons}. The usually short-lived bubble can be dynamically temporarily stabilized, which explains their importance in the dynamics of $Q$-balls. This happens due to the excitation of massless Goldstone modes, which, exerting pressure on the bubble boundaries or being trapped as bound modes, prevent the bubble from collapsing.