Related papers: Wobbling kinks in $\phi^4$ theory
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 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…
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 dynamics of a wobbling kink in a two-component coupled $\phi^4$ scalar field theory (with an excited orthogonal shape mode) is addressed. For this purpose, the vibration spectrum of the second order small kink fluctuation is studied in…
In this paper the scattering between a wobbling kink and a wobbling antikink in the standard $\phi^4$ model is numerically investigated. The dependence of the final velocities, wobbling amplitudes and frequencies of the scattered kinks on…
The Fourth order $\phi^4$ model generalizes the classical $\phi^4$ model of quantum field theory, sharing the same kink solution. It is also the dispersive counterpart of the well-known parabolic Cahn-Hilliard equation. Mathematically…
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…
Asymptotic behaviour of eigenvalues and eigenfunctions of a stiff problem is described in the case of the fourth-order ordinary differential operator. Considering the stiffness coefficient that depends on a small parameter epsilon and…
A particle-triaxial rigid core Hamiltonian is semi-classically treated. The coupling term corresponds to a particle rigidly coupled to the triaxial core, along a direction that does not belong to any principal plane of the inertia…
A triaxial core rotating around the middle axis, i.e. 2-axis, is cranked around the 1-axis, due to the coupling of an odd proton from a high j orbital. Using the Bargmann representation of a new and complex boson expansion of the angular…
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 motion of a triaxial rotor coupled to a high-j quasiparticle is treated semiclassi- cally. Longitudinal and transverse coupling regimes can be distinguished depending on, respectively, whether the quasiparticle angular momentum…
The wobbling motion excited on triaxial superdeformed nuclei is studied in terms of the cranked shell model plus random phase approximation. Firstly, by calculating at a low rotational frequency the \gamma-dependence of the three moments of…
The entanglement and coherence of the wobbling mode are studied in the framework of the particle plus triaxial rotor model for the one-quasiparticle nucleus $^{135}$Pr and the two-quasiparticles nucleus $^{130}$Ba. The focus lies on the…
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…
We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical…
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…
In the present work we construct kink solutions for different (parabolic and wave) variants of the fractional $\phi^4$ model, in both the sub-Laplacian and super-Laplacian setting. We establish existence and monotonicity results (for the…
The lambda-phi4 kink is linearly and topologically stable. We study how extra energy perturbations are dissipated beyond the linear regime. We found that depending on the width, amplitude and energy of a Gaussian perturbation different…
We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant…