Related papers: Kink Dynamics in a Topological Phi^4 Lattice
In this work, we investigate the dynamics of a scalar field in the nonintegrable $\displaystyle \phi ^{4}$ model, restricted to the half-line. Here we consider singular solutions that interpolate the Dirichlet boundary condition…
This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking…
By means of dynamical mean field theory calculations, it was recently discovered that kinks generically arise in strongly correlated systems, even in the absence of external bosonic degrees of freedoms such as phonons. However, the physical…
There is a growing interest in searching for topology in fractal dimensions with the aim of finding different properties and advantages compared to the integer dimensional case. It has previously been shown that the Laughlin state can be…
We consider a $(1+1)$-dimensional theory with a single real scalar field $\phi$ whose kinematics is modified by a generalizing function $f(\phi)$. After briefly reviewing its Bogomol'nyi-Prasad-Sommerfield (BPS) structure, we focus on a…
The unitarity of the 4D lattice theory of gravity in the case of the Minkowski signature is proved. The proof is valid only for lattices that conserve the number of degrees of freedom during time evolution. The Euclidean signature and the…
When a self-localized quasiparticle excitation propagates along a discrete one dimensional lattice, it becomes subject to a dissipation that converts the kinetic energy into lattice vibrations. Eventually the kinetic energy does no longer…
The behavior of the kink in the sine-Gordon (sG) model in the presence of periodic inhomogeneity is studied. An ansatz is proposed that allows for the construction of a reliable effective model with two degrees of freedom. Effective models…
We investigate an integrable property and observables of 2 dimensional N=(4,4) topological field theory defined on a discrete lattice by using the "orbifolding" and "deconstruction" methods. We show that our lattice model possesses the…
By considering specific limits in the gauge coupling constant of pure Yang--Mills dynamics, it is shown how there exist topological quantum field theory sectors in such systems defining nonperturbative topological configurations of the…
The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady…
Recently a linearized perturbation theory has been formulated for soliton sectors of quantum field theories. While it is more economical than alternative formalisms, such as collective coordinates, it is currently limited to solitons which…
This paper concerns classical nonlinear scalar field models on the real line. If the potential is a symmetric double-well, such a model admits static solutions called kinks and antikinks, which are perhaps the simplest examples of…
Magnetic skyrmions are chiral spin structures with non-trivial topology that comprise two-dimensional quasi-particles and are promising information carriers for data storage and processing devices. Skyrmion lattices in magnetic thin films…
We consider nonlinear Klein-Gordon wave equations and illustrate that standard discretizations thereof (involving nearest neighbors) may preserve either standardly defined linear momentum or total energy but not both. This has a variety of…
To obtain the one-loop corrections to the mass of a kink by mode regularization, one may take one-half the result for the mass of a widely separated kink-antikink (or sphaleron) system, where the two bosonic zero modes count as two degrees…
The main focus of the present work is to study quasi-one-dimensional kink-antikink stripes embedded in the two-dimensional sine-Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink…
In this paper we use 1D quantum mechanical systems with Higgs-like interaction potential to study the emergence of topological objects at finite temperature. Two different model systems are studied, the standard double-well potential model…
The O(3) sigma model and abelian Higgs model in two space dimensions admit topological (Bogomol'nyi) lower bounds on their energy. This paper proposes lattice versions of these systems which maintain the Bogomol'nyi bounds. One consequence…
We develop the approach to the problem of integrable discretization based on the notion of $r$--matrix hierarchies. One of its basic features is the coincidence of Lax matrices of discretized systems with the Lax matrices of the underlying…