Kinks and realistic impurity models in φ4-theory

Abstract

The [Formula: see text]-theory is ubiquitous as a low-energy effective description of processes in all fields of physics, ranging from cosmology and particle physics to biophysics and condensed matter theory. The topological defects, or kinks, in this theory describe stable, particle-like excitations. In practice, these excitations will necessarily encounter impurities or imperfections in the background potential as they propagate. Here, we describe the interaction between kinks and various types of realistic impurity models. We find that realistic impurities behave qualitatively like the well-studied, idealized delta function impurities, but that significant quantitative differences appear in both the characteristics of localized impurity modes, and in the collision dynamics. We also identify a particular regime of kink-impurity interactions, in which kinks lose all of their kinetic energy upon colliding with an impurity.

Emergence of oscillons in kink-impurity interactions

“…First of all, we showed that an internal mode of the impurity could be excited at high initial velocities for an attractive impurity. The observed values for the impurity mode frequency match theoretical and numerical results reported earlier in the study of a single kink interacting with a localized impurity [23,33], which shows the excitation to be a property of the impurity that is independent of its excitation conditions.…”

“…They leave behind an oscillating mode, localized at the site of the impurity, x = 0. Similar impurity modes have been observed in numerical simulations of kink-impurity interactions [23,33], and found analytically for a Dirac-delta impurity [23], where its time-dependent profile δϕ(t, x) was predicted to be:…”

“…First, for special values of the initial velocity, we encounter resonances, in which the kink and antikink escape to infinity after a finite number of collisions. This is in stark contrast to kink-impurity interactions [23,33], in which resonances are observed only for attractive impurities. Here, we find them at various repulsive impurity strengths and initial velocity, such as = −0.8 (v in = 0.771, v in = 0.772) and = −0.4 (v in = 0.540, v in = 0.555, v in = 0.557).…”

Scattering of kinks in the $Bφ^{4}$ model

“…Interestingly, the DSG system is used for the description of some physical systems such as gold dislocations [37], optical pulses [38], and Josephson structures [39]. The ϕ 4 system and its deformed versions have been widely studied due to their simplicity and applications [25,[40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. In relation to the study of kink-antikink scattering and the quasi-fractal structure, the ϕ 4 system has been considered as a representative of such non-integrable systems [40][41][42][43][44][45][46].…”

“…In relation to the study of kink-antikink scattering and the quasi-fractal structure, the ϕ 4 system has been considered as a representative of such non-integrable systems [40][41][42][43][44][45][46]. It has been studied from different aspects including the interaction of kinks with impurities [47][48][49][50], maximum values of quantities at the center of mass in a kink-antikink collision [51], scattering between wobbling kink and antikink [52][53][54], the standard deformed versions developed by Bazeia and Losano [55][56][57][58][59], and collective coordinate models for kink-antikink interactions [45,46]. Recently, models with polynomial potentials of higher degrees have also received a lot of attention including the ϕ 6 model [60][61][62][63], the ϕ 8 model [64][65][66][67], and the models that yield kinks with powerlaw tails [69][70][71].…”