Related papers: Moving Kinks and Their Wave Packets
Recently we introduced a local photon approach for modelling the quantised electromagnetic field in position space. Using this approach, we define the momentum of light in this paper as in quantum mechanics as the generator for spatial…
We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position…
The problem of stability and spectrum of linear excitations of a soliton (kink) of the dispersive sine-Gordon and $\varphi^4$ - equations is solved exactly. It is shown that the total spectrum consists of a discrete set of frequencies of…
This paper presents a quantum field theoretical formalism for studying magnons in finite nanostructures with arbitrary shapes and spatially nonuniform ground states. It extends the classical micromagnetic formalism by introducing a…
This paper investigates the existence of traveling--wave--type patterns in the Keller--Segel model with logarithmic sensitivity. We consider both the linear diffusion case and the nonlinear, flux-saturated diffusion of relativistic…
We study various properties of topological solitons (kinks) of a field-theoretic model with a polynomial potential of the twelfth degree. This model is remarkable in that it has several topological sectors, in which kinks have different…
We study quantum percolation which is described by a tight-binding Hamiltonian containing only off-diagonal hopping terms that are generally in quenched binary disorder (zero or one). In such a system, transmission of a quantum particle is…
We analyse two issues that arise in the context of (matrix) string theories in plane wave backgrounds, namely (1) the use of Brinkmann- versus Rosen-variables in the quantum theory for general plane waves (which we settle conclusively in…
In this report, fundamental educational concepts of linear and non-linear equations and solutions of nonlinear equations from the book High-Temperature Superconductivity: The Nonlinear Mechanism and Tunneling Measurements (Kluwer Academic…
A dislocation, just like a phonon, is a type of atomic lattice displacement but subject to an extra topological constraint. However, unlike the phonon which has been quantized for decades, the dislocation has long remained classical. This…
Wave particle duality remains a central interpretational challenge in quantum theory. In this work, we develop a trajectory-based description of photon dynamics formulated in an extended complex space within the relativistic quantum…
The forced soliton equation is the starting point for semiclassical computations with solitons away from the small momentum transfer regime. This paper develops necessary analytical and numerical tools for analyzing solutions to the forced…
In this series of lectures a method is developed to compute one-loop shifts to classical masses of kinks, multi-component kinks, and self-dual vortices. Canonical quantization is used to show that the mass shift induced by one-loop quantum…
We study localized traveling waves and chaotic states in strongly nonlinear one-dimensional Hamiltonian lattices. We show that the solitary waves are super-exponentially localized, and present an accurate numerical method allowing to find…
In a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have…
We construct center-stable and center-unstable manifolds, as well as stable and unstable manifolds, for the nonlinear Klein-Gordon equation with a focusing energy sub-critical nonlinearity, associated with a family of solitary waves which…
A new kinematic condition for soliton motions of an $n$-dimensional continuum in $R^{n+m}$, independent of the underlying physics, is proven. The condition and its consequences for different cases are demonstrated. A soliton in a 1D string…
A wave-function framework for the theory of the (e,e'N) reaction is presented in order to justify the use of coupled channel equations in the usual Feynman matrix element. The overall wave function containing the electron and nucleon…
The soliton resolution conjecture states that solutions to solitonic equations with generic initial data should, after some non--linear behaviour, eventually resolve into a finite number of solitons plus a radiative term. This conjecture is…
We present and study new mechanism of interaction between the solitons based on the exchange interaction mediated by the localized fermion states. As particular examples, we consider solutions of simple 1+1 dimensional scalar field theories…