False vacuum decay in kink scattering

Abstract

In this work we consider kink-antikink and antikink-kink collisions in a modified φ 4 model with a false vacuum characterized by a dimensionless parameter ǫ. The usual φ 4 model is recovered for ǫ = 0. We investigate the ǫ << 1 regime where the kink in the presence of false vacuum can be understood as a small deformation of the standard kink for the φ 4 model. We show that the attractive interaction between the kink-antikink pair leads to a rich scattering pattern, in some cases delaying considerably the false vacuum decay.

Resonance structures in kink-antikink collisions in a deformed sine-Gordon model

“…Nevertheless, for small values of the parameter 0.05 the potential retains a false vacuum at φ ≈ −2π (along with its Z 2 reflection at φ ≈ 4π), as illustrated in figure 1. The presence of such false vacua significantly affects the dynamics of the kinks [30,31] with them enable a smooth transition from the situation for > 0 back to sine-Gordon scattering at = 0. Figure 8 shows a collection of space-time maps of the scalar field through the collision process.…”

“…After the initial collision the new kinks bounding the false vacuum region move apart and decelerate [31,35], stopping at the turning points x = ±L/2 where the volume energy 16π 2 L of the bubble together with the bubble wall surface energy E σ becomes equal to the initial kinetic energy of the colliding kinks, i.e.…”

Quasinormal modes in kink excitations and kink–antikink interactions: a toy model

“…Resonance windows are found in many other kink and antikink scattering models including recently the φ 4 model variants [30][31][32], the φ 6 model and variants [33][34][35], the φ 8 model [36,37], coupled two component kinks [38,39] and other models [40]. In all these works the presence of vibrational modes is an essential ingredient to find resonance windows.…”

Semi-compactness and multiple oscillating pulses in kink scattering

“…Kink scattering has been investigated in several models. One can cite the polynomials with one scalar field, for instance, modified φ 4 model [23][24][25], φ 6 model [26][27][28], φ 8 model [29][30][31], nonpolynomial [32][33][34][35], models which possess kinks with power-law tails [36][37][38] and models with two scalar fields [39][40][41][42][43][44]. Furthermore, there are studies of kink collision with a boundary [45][46][47], with impurities [48][49][50][51][52], multi-kink collision [53][54][55][56] and other models [57][58][59][60][61].…”