Related papers: Wobbling kinks and shape mode interactions in a co…
In this paper the interaction between the shape modes of the wobbling kinks arising in the family of two-component MSTB scalar field theory models is studied. The spectrum of the second order small kink fluctuation in this model has two…
The resonant energy transfer mechanism, responsible for the presence of fractal patterns in the velocity diagrams of kink-antikink scattering, is analyzed for a family of two-component scalar field theory models, in which the kink solutions…
The wobbling kink is the soliton of the $\phi^4$ model with an excited internal mode. We outline an asymptotic construction of this particle-like solution that takes into account the coexistence of several space and time scales. The…
This thesis presents an extensive analysis of the behavior of topological solitons when one or more of their internal modes are activated. The first part of this manuscript is devoted to the study of the simplest topological solitons in…
We present a uniform asymptotic expansion of the wobbling kink to any order in the amplitude of the wobbling mode. The long-range behaviour of the radiation is described by matching the asymptotic expansions in the far field and near the…
Many kink solutions enjoy internal excitations, called shape modes. In some 1+1d scalar models, such as the $\phi^4$ double-well model, when a kink's shape mode is excited twice it may decay to a ground state kink plus a meson. We…
We study the collision of a kink and an antikink in the double sine-Gordon model with and without the excited vibrational mode. In the latter case, we find that there is a limited range of the parameters where the resonance windows exist,…
The amplitude of oscillations of the freely wobbling kink in the $\phi^4$ theory decays due to the emission of second-harmonic radiation. We study the compensation of these radiation losses (as well as additional dissipative losses) by the…
The $\phi^4$ double-well theory admits a kink solution, whose rich phenomenology is strongly affected by the existence of a single bound excitation called the shape mode. We find that the leading quantum correction to the energy needed to…
In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In…
We analytically sum the leading bubble diagrams that contribute to the elastic scattering amplitude of a kink and a meson in the $\phi^4$ double-well model. We find a single peak, corresponding to the unstable kink state in which the shape…
Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. As an important step towards the observation of entanglement between propagating microwave photons we demonstrate the…
We present a numerical study of the process of the kink-antikink collisions in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal two different soliton solutions which represent double kink configuration and…
The asymmetric scattering between wobblers and kinks in the standard $\phi^4$ model is numerically investigated in two different scenarios. First, the collision between wobblers with opposite phase is analyzed. Here, a destructive…
The radiation from oscillating kink in (1+1) dimensional relativistic $\phi^4$ model is considered. Both analytical and numerical approaches are presented and the comparison between these methods is discussed. Acceleration of the kink in…
The system consisting of a fermion in the background of a wobbling kink is studied in this paper. To investigate the impact of the wobbling on the fermion-kink interaction, we employ the time-dependent perturbation theory formalism in…
We analyze a mechanism of coupling of high- and low-$K$ bands in terms of a dynamical treatment for nuclear rotations, i.e.,wobbling motion. The wobbling states are produced through the generator coordinate method after angular momentum…
The method of multiple scales is used to study the wobbling kink of the $\phi^4$ equation. The amplitude of the wobbling is shown to decay very slowly, as $t^{-1/2}$, and hence the wobbler turns out to be an extremely long-lived object.
The amplitude of an excited shape mode in a kink is expected to decay with a well-known power law via scalar radiation emission due to the nonlinear self-coupling of the scalar field. In this work we propose an alternative decay mechanism…
We consider a rational scalar field model in (1+1)-dimensions where the long-range character of the kinks is controllable. We show via numerical simulations that kinks with long-range tails on both sides can exhibit resonance windows. The…