Kink Collisions Research Articles

Numerical Simulation of Kink Collisions, Analytical Solutions and Conservation Laws of the Potential Korteweg–de Vries Equation

Numerical Simulation of Kink Collisions, Analytical Solutions and Conservation Laws of the Potential Korteweg–de Vries Equation

A toy model to explain the missing bounce windows in the kink-antikink collisions

We propose a toy model to reproduce the fractal structure of kink and antikink collisions on one topological sector of ϕ6 theory. Using the toy model, we investigate the missing bounce windows observed in the fractal structure, and show that the coupling between two oscillation modes modulate the emergence of the missing bounce windows. By numerical calculation, we present that the two bounce resonance corresponds to the lower eigenfrequency of the toy model.

Localized structures in three-field models: Geometrically constrained configurations and the first-order framework

This work deals with models described by three real scalar fields in one spatial dimension. We study the case where two of the three fields engender kinematical modifications, which respond as geometrical constrictions, that can be used to change the center and/or the tails of the kinklike configurations. An important advantage of our procedure is the construction of a method for the obtention of first-order differential equations that solve the equations of motion and give rise to stable localized structures. We illustrate the general procedure investigating several distinct examples, and suggesting some possibilities of applications of practical use, in particular, to the case of domain walls and skyrmions in magnetic material, collisions of kinks and to deal with braneworld scenarios having a warped five-dimensional anti de Sitter geometry, with a single extra dimension of infinite extent.

Abundant dynamical solitary waves through Kelvin-Voigt fluid via the truncated M-fractional Oskolkov model

This effort explores the dynamic behavior of solitary wave fronts using the Oskolkov model in a truncated M-fractional derivative form. This effort has been performed through the application of modified extended tanh and a novel form of modified Kudryashov techniques. All obtained solutions manifest in the form of sinusoidal, hyperbolic, and constant basis function solutions within the fractional model. Within this framework, the applied techniques yield various solitary wave structures, including bright and dark bell solitons, kinks, anti-kinks, linked lumps, and collisions of kinks. Additionally, they produce singular kink solitons and lump waves. The effects of fractionality and the coefficient of the highest-order derivative are depicted in Figs. 1 through 11. Moreover, all figures are organized to illustrate the properties of the innovative soliton wave propagations. The studies have also revealed that the fractional Oskolkov model can support both fundamental and higher-order solitons, each characterized by distinct properties and highly efficient behaviors. Various dynamical solitary waves obtained here can be described transmission waves through Kelvin-Voigt fluid with real happenings as it represented by fractional form.

Mechanization of a scalar field theory in 1+1 dimensions: Bogomol'nyi-Prasad-Sommerfeld mechanical kinks and their scattering.

We present an updated version of a general-purpose collective coordinate model that aims to fully map out the dynamics of a single scalar field in 1+1 dimensions. This is achieved by a procedure that we call a mechanization, in which we reduce the infinite number of degrees of freedom down to a finite and controllable number by chopping the field into flat segments connected via joints. In this paper we introduce two new ingredients to our procedure. The first is a manifestly Bogomol'nyi-Prasad-Sommerfeld (BPS) mechanization in which BPS mechanical kinks saturate the same bound on energy as their field-theoretic progenitors. The second is allowing the joints to switch, leading to an extended concept of the effective Lagrangian, through which we describe direct collisions of mechanical kinks and antikinks.

Collisions of weakly-bound kinks in the Christ-Lee model

We investigate soliton collisions in a one-parameter family of scalar field theories in 1+1 dimensions which was first discussed by Christ and Lee [1]. The models have a sextic potential with three local minima, and for suitably small values of the parameter their kinks have an internal structure in the form of two weakly-bound subkinks. We show that for these values of the parameter kink collisions are best understood as an independent sequence of collisions of these subkinks, and that a static mode analysis is not enough to explain resonant structures emerging in this model. We also emphasise the role of radiation and oscillon formation in the collision process.

Relativistic moduli space and critical velocity in kink collisions.

One important tool in the analysis of the collision of kinks and other topological solitons is the reduction of the original field theory to a finite-dimensional system of so-called collective coordinates. Here we study one recent proposal of a collective coordinate model (CCM), the perturbative relativistic moduli space (pRMS), where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyze the possibility to calculate within the pRMS the critical velocity, i.e., the initial velocity of kinks at which single bounce scattering changes into a multibounce or annihilation collision. We find that for a growing number of Derrick modes the critical velocity of the CCM approaches the full field theory value. In particular, in the case of the ϕ^{4} model we reach a 99% accuracy. We also see this convergence for a wide range of models belonging to the family of the double sine-Gordon and Christ-Lee theories, especially in those cases where the kinks do not reveal a too well-pronounced half-kink inner structure.

Moduli Space for Kink Collisions with Moving Center of Mass

We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the mutual distance and the position of the center of mass) is of a wormhole type, whose throat shrinks to a point for symmetric kinks. In this case, a singularity is formed. For non-zero momentum, it prohibits solutions where the solitons pass through each other. We show that this unphysical feature can be cured by enlarging the dimension of the moduli space, e.g., by the inclusion of internal modes.

Fermionic spectral walls in kink collisions

We show that a spectral wall, i.e., an obstacle in the dynamics of a bosonic soliton, which arises due to the transition of a normal mode into the continuum spectrum, exists after coupling the original bosonic model to fermions. This spectral wall can be experienced if the boson or fermion field is in an excited state. Furthermore, while passing through a spectral wall, an incoming kink-fermion bound state can be separated into purely bosonic kink, which continues to move to spatial infinity and a fermionic cloud that spreads in the region before the wall.

Kink collision in the noncanonical [formula omitted] model: A model with localized inner structures

We study collisions of kinks in the one-space and one-time dimensional noncanonical nonintegrable scalar ϕ6 model. We examine the energy density of the kink, and we find that, as a function of the parameters that control the curvature of the potential, a localized inner structure of the energy density emerges. We also examine the kink excitation spectrum and the dynamics of the kink collisions for a wide range of initial velocities. We find that apart from the resonance windows, the production of two to three oscillons occurs for some values of the principal parameters of the model.

Collisions of kinks in deformed [formula omitted] and [formula omitted] models

Two hyperbolic-deformed field theoretic models are discussed. In both of them, due to the effect of specific deformation function on the well known φ4 and φ6 models, their internal structure may change significantly. Unlike the φ4 kinks solutions, which has only one internal mode in addition to its translational mode, the kinks of the hyperbolic-deformed φ4 model can have several internal modes. Moreover, the deformation on the φ6 model has other interesting features, because the kinks of the φ6 model have only a zero mode and the deformation may cause the appearance of internal mode for both kink and antikink. The presence of the new internal modes modify the collisions which we explore in the present work. The deformation relies on a real parameter, which controls the number of internal modes, and we also study how the deformation parameter alter the mass of the kinks and the critical velocities involved in the collisions.

Kink Collision in the Noncanonical Φ⁶ Model: A Model with Localized Inner Structures

Kink Collision in the Noncanonical Φ⁶ Model: A Model with Localized Inner Structures

Fractal structure of the soliton scattering for the graphene superlattice equation

The graphene superlattice equation, a modified sine-Gordon equation, governs the propagation of solitary electromagnetic waves in a graphene superlattice. This equation has kink solutions without explicit analytical expression, requiring the use of quadrature methods. The inelastic collision of kinks and antikinks with the same but opposite speed is studied numerically for the first time; after their interaction they escape to infinity when its speed is either larger than a critical value or it is inside a series of resonance windows; otherwise, they form a breather-like state that slowly decays by radiating energy. Here, the fractal structure of these resonance windows is characterized by using a multi-index notation and their main features are compared with the predictions of the resonant energy exchange theory showing good agreement. Our results can be interpreted as new evidence in favour of this theory.

Mass and spin for classical strings in dS3

We demonstrate that all rigidly rotating strings with center of mass at the origin of the dS3 static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser’s algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin < 1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.

An introduction to kinks in $\varphi^4$-theory

As a low-energy effective model emerging in disparate fields throughout all of physics, the ubiquitous \varphi^4φ4-theory is one of the central models of modern theoretical physics. Its topological defects, or kinks, describe stable, particle-like excitations that play a central role in processes ranging from cosmology to particle physics and condensed matter theory. In these lecture notes, we introduce the description of kinks in \varphi^4φ4-theory and the various physical processes that govern their dynamics. The notes are aimed at advanced undergraduate students, and emphasis is placed on stimulating qualitative insight into the rich phenomenology encountered in kink dynamics. The appendices contain more detailed derivations, and allow enquiring students to also obtain a quantitative understanding. Topics covered include the topological classification of stable solutions, kink collisions, the formation of bions, resonant scattering of kinks, and kink-impurity interactions.

Quasinormal modes in kink excitations and kink\u2013antikink interactions: a toy model

We study excitations and collisions of kinks in a scalar field theory where the potential has two minima with Z_2 symmetry. The field potential is designed to create a square well potential in the stability equation of the kink excitations. The stability equation is analogous to the Schrödinger equation, and therefore we use quantum mechanics techniques to study the system. We modify the square well potential continuously, which allows the excitation to tunnel and consequently turns the normal modes of the kink into quasinormal modes. We study the effect of this transition, leading to energy leak, on isolated kink excitations. Finally, we investigate kink–antikink collisions and the resulting scaling and fractal structure of the resonance windows considering both normal and quasinormal modes and compare the results.

Collision of two kinks with inner structure

In this work, we study kink collisions in a scalar field model with scalar-kinetic coupling. This model supports kink/antikink solutions with inner structure in the energy density. The collision of two such kinks is simulated by using the Fourier spectral method. We numerically calculate how the critical velocity and the widths of the first three two bounce windows vary with the model parameters. After that, we report some interesting collision results including two-bion escape final states, kink-bion-antikink intermediate states and kink or antikink intertwined final states. These results show that kinks with inner structure in the energy density have similar properties as those of the double kinks.

Kink scattering in hyperbolic models

In this work, we study kink–antikink and antikink–kink collisions in hyperbolic models of fourth and sixth orders. We compared the patterns of scattering with known results from polynomial models of the same order. The hyperbolic models considered here tend to the polynomial [Formula: see text] and [Formula: see text] models in the limit of small values of the scalar field. We show that kinks and antikinks that interact hyperbolically with the fourth order differ sensibly from those governed by the polynomial [Formula: see text] model. The increasing of the order of interaction to the sixth order shows that the hyperbolic and polynomial models give intricate structures of scattering that differ only slightly. The dependence on the order of interaction is related to some characteristics of the models such as the potential of perturbations and the number of vibrational modes.

Estimation of diffusional effects on solution hardening at high temperatures in single phase compositionally complex body centered cubic alloys

Solution hardening in body centered cubic alloys as a function of temperature can be well described by the Suzuki model. This model includes significant strengthening from the dragging of edge dislocation dipoles produced by kink collisions along the screw dislocations. However, the model does not consider diffusion-controlled processes. Here we estimate a critical temperature Tcr above which diffusional effects become important, resulting in the collapse of edge dipoles. Loss of edge dipoles leads to a significant decrease in yield strength above Tcr and marks the temperature limit for structural applications of these single phase body centered cubic alloys.

Decay of Cosmic String Loops due to Particle Radiation

Constraints on the tension and the abundance of cosmic strings depend crucially on the rate at which they decay into particles and gravitational radiation. We study the decay of cosmic string loops in the Abelian-Higgs model by performing field theory simulations of loop formation and evolution. We find that our set of string loops emits particle radiation primarily due to kink collisions, and that the decay time due to these losses is proportional to L^{p} with p≈2 where L is the loop length. In contrast, the decay time to gravitational radiation scales in proportion to L, and we conclude that particle emission is the primary energy loss mechanism for loops smaller than a critical length scale, while gravitational losses dominate for larger loops.