Scattering of kinks in Frankensteinian potentials: Kinks as bubbles of exotic mass and phase transitions in oscillon production

Abstract

We present a dynamical picture of kink-anti-kink scattering in a pair of special, Frankensteinian potentials made of piece-wise quadratic and linear pieces. Specifically, we focus on models that support kinks without skin and core regions. We propose an intuitive interpretation for these models as being essentially free massive theories with a built-in particle-pair like production mechanism that enters into the dynamics above certain field-value thresholds. We present results concerning the kink's characteristics depending on these thresholds and the distribution of bouncing windows. We show that the second model exhibits a phase-transition-like property in which the nature of collisions switches from disintegration into a massive wave to production of oscillons for large segments of initial velocities when the field threshold is low enough.

Figures (23)

• Figure 1: The simplest Frankensteinian potentials and their corresponding kinks. The vacua are placed at $\pm 1$, and kinks are centered at $x=0$ for simplicity. The labels enumerate the structural pieces of the kinks with T = tail, S = skin, and C = core.
• Figure 2: The TCT potential for a generic value of the sewing point $0<\beta<1$ (solid) and the two limits $\beta =0$ (dashed) and $\beta =1$ (dotted).
• Figure 3: Upper panel: A TCT kink, centered at origin $x=0$, made of two exponentially decaying tails and a sine core that are glued differentiably at $x = \pm x_0$. Lower panel: Field density plot of a traveling TCT kink, the colors indicate which 'type' of field is present. Blue and red represent the Klein-Gordon fields near -1 and +1 vacua, while gold color stands for the 'exotic' negative mass field. Here $\beta = 0.6$.
• Figure 4: Dependence of the mass, size of the core and the Derrick frequency on the sewing point $\beta$.
• Figure 5: Number of bound modes for TCT as depending on $\beta$.