Related papers: An introduction to kinks in $\varphi^4$-theory
In this work we study the presence of kinks in models described by a single real scalar field in bidimensional spacetime. We work within the first-order framework, and we show how to write first-order differential equations that solve the…
Numerical study of order parameter dynamics in the course of second order (Landau-Ginzburg) symmetry breaking transitions shows that the density of topological defects, kinks, is proportional to the fourth root of the rate of the quench.…
We study kink-antikink scattering in a one-parameter variant of the $\phi^4$ theory where the model parameter controls the static intersoliton force. We interpolate between the limit of no static force (BPS limit) and the regime where the…
Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to…
The application of variational principles for analyzing problems in the physical sciences is widespread. Cantilever-like problems, where one end is fixed and the other end is free, have received less attention in terms of their stability…
It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a…
Rigid body interactions are fundamental to numerous scientific disciplines, but remain challenging to simulate due to their abrupt nonlinear nature and sensitivity to complex, often unknown environmental factors. These challenges call for…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases…
We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system…
The topological theory of phase transitions has its strong point in two theorems proving that, for a wide class of physical systems, phase transitions necessarily stem from topological changes of some submanifolds of configuration space. It…
We obtain exact solutions for kinks in $\phi^{8}$, $\phi^{10}$ and $\phi^{12}$ field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…
In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…
Particles propagating in de Sitter spacetime can be described by the topological BF $\SO(4,1)$ theory coupled to point charges. Gravitational interaction between them can be introduced by adding to the action a symmetry breaking term, which…
To show that steadily propagating nonlinear waves in active matter can be driven internally, we develop a prototypical model of a topological kink moving with a constant supersonic speed. We use a model of a bi-stable mass-spring (FPU)…
We study the elasticity of the collision of two kinks with an incoming low speed $v\in (0,1)$ for the nonlinear wave equation in dimension $1+1$ known as the $\phi^{6}$ model. We prove for any $k\in\mathbb{N}$ that if the incoming speed $v$…
We present a dynamical picture of kink-anti-kink scattering in a pair of special, Frankensteinian potentials made of piece-wise quadratic and linear pieces. Specifically, we focus on models that support kinks without skin and core regions.…
The spontaneous nucleation and dynamics of topological kink defects have been studied in trapped arrays of 41-43 Yb ions. The number of kinks formed as a function of quench rate across the linear-zigzag transition is measured in the…
Following Finkelstein and Misner, kinks are non-trivial field configurations of a field theory, and different kink-numbers correspond to different disconnected components of the space of allowed field configurations for a given topology of…