arXiv subjects
Publications and source records attributed to P. Klimas.
We present a class of solutions of the CPN model in (3+1) dimensions. We suggest that they represent vortex-like configurations. We also discuss some of their properties. We show that some configurations of vortices have a divergent energy per unit length while for the others such an energy has a minimum for a very special orientation of vortices. We also discuss the Noether charge densities of these vortices.
We consider a four dimensional field theory with target space being CP^N which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP^1. We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x^1+i x^2) and (x^3+x^0) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.
For the baby Skyrme model with a specific potential, compacton solutions, i.e., configurations with a compact support and parabolic approach to the vacuum, are derived. Specifically, in the non-topological sector, we find spinning Q-balls and Q-shells, as well as peakons. Moreover, we obtain compact baby skyrmions with non-trivial topological charge. All these solutions may form stable multi-soliton configurations provided they are sufficiently separated.
We study a scalar field theory with a non-standard kinetic term minimally coupled to gravity. We establish the existence of compact boson stars, that is, static solutions with compact support of the full system with self-gravitation taken into account. Concretely, there exist two types of solutions, namely compact balls on the one hand, and compact shells on the other hand. The compact balls have a naked singularity at the center. The inner boundary of the compact shells is singular, as well, but it is, at the same time, a Killing horizon. These singular, compact shells therefore resemble black holes.
Some models providing shell-shaped static solutions with compact support (compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding exact solutions are calculated analytically. These solutions turn out to be topological solitons, and may be classified as maps $S^3 \to S^3$ and suspended Hopf maps, respectively. The Lagrangian of these models is given by a scalar field with a non-standard kinetic term (K field) coupled to a pure Skyrme term restricted to $S^2$, rised to the appropriate power to avoid the Derrick scaling argument. Further, the existence of infinitely many exact shell solitons is explained using the generalized integrability approach. Finally, similar models allowing for non-topological compactons of the ball type in 3+1 dimensions are briefly discussed.
We investigate a version of the abelian Higgs model with a non-standard kinetic term (K field theory) in 2+1 dimensions. The existence of vortex type solutions with compact support (topological compactons) is established by a combination of analytical and numerical methods. This result demonstrates that the concept of compact solitons in K field theories can be extended to higher dimensions.
A procedure allowing for the construction of Lorentz invariant integrable models living in d+1 dimensional space-time and with an n dimensional target space is provided. Here, integrability is understood as the existence of the generalized zero-curvature formulation and infinitely many conserved quantities. A close relation between the Lagrange density of the integrable models and the pullback of the pertinent volume form on target space is established. Moreover, we show that the conserved currents are Noether currents generated by the volume preserving diffeomorphisms. Further, we show how such models may emerge via abelian projection of some gauge theories. Then we apply this framework to the construction of integrable models with exotic textures. Particularly, we consider integrable models providing exact suspended Hopf maps i.e., solitons with a nontrivial topological charge of pi_4(S^3). Finally, some families of integrable models with solitons of pi_n(S^n) type are constructed. Infinitely many exact solutions with arbitrary value of the topological index are found. In addition, we demonstrate that they saturate a Bogomolny bound.
Recently we proposed that K fields, that is, fields with a non-standard kinetic term, may provide a mechanism for the generation of thick branes, based on the following observations. Firstly, K field theories allow for soliton solutions with compact support, i.e., compactons. Compactons in 1+1 dimensions may give rise to topological defects of the domain wall type and with finite thickness in higher dimensions. Secondly, propagation of linear perturbations is confined inside the compacton domain wall. Further, these linear perturbations inside the topological defect are of the standard type, in spite of the non-standard kinetic term. Thirdly, when gravity is taken into account, location of gravity in the sense of Randall--Sundrum works for these compacton domain walls provided that the backreaction of gravity does not destabilize the compacton domain wall. It is the purpose of the present paper to investigate in detail the existence and stability of compacton domain walls in the full K field and gravity system, using both analytical and numerical methods. We find that the existence of the domain wall in the full system requires a correlation between the gravitational constant and the bulk cosmological constant, which is thoroughly analyzed.
We present explicit solutions of the signum-Gordon scalar field equation which have finite energy and are periodic in time. Such oscillons have a strictly finite size. They do not emit radiation.
Three new models with V-shaped field potentials $U$ are considered: a complex scalar field $X$ in 1+1 dimensions with $U(X)= |X|$, a real scalar field $Φ$ in 2+1 dimensions with $U(Φ) = |Φ|$, and a real scalar field $ϕ$ in 1+1 dimensions with $U{ϕ) = ϕΘ(ϕ)$ where $Θ$ is the step function. Several explicit, self-similar solutions are found. They describe interesting dynamical processes, for example, `freezing' a string in a static configuration.
We investigate self-similar solutions of evolution equation of a (1+1)-dimensional field model with the V-shaped potential $U(ϕ) = | ϕ|,$ where $ϕ$ is a real scalar field. The equation contains a nonlinear term of the form $sign(ϕ)$, and it possesses a scaling symmetry. It turns out that there are several families of the self-similar solutions with qualitatively different behaviour. We also discuss a rather interesting example of evolution with non self-similar initial data - the corresponding solution contains a self-similar component.
We investigate a (1+1)-dimensional nonlinear field theoretic model with the field potential $V(ϕ)| = |ϕ|.$ It can be obtained as the universal small amplitude limit in a class of models with potentials which are symmetrically V-shaped at their minima, or as a continuum limit of certain mechanical system with infinite number of degrees of freedom. The model has an interesting scaling symmetry of the 'on shell' type. We find self-similar as well as shock wave solutions of the field equation in that model.
In this lecture we outline the main results of our investigations of certain field-theoretic systems which have V-shaped field potential. After presenting physical examples of such systems, we show that in static problems the exact ground state value of the field is achieved on a finite distance - there are no exponential tails. This applies in particular to soliton-like object called the topological compacton. Next, we discuss scaling invariance which appears when the fields are restricted to small amplitude perturbations of the ground state. Evolution of such perturbations is governed by nonlinear equation with a non-smooth term which can not be linearized even in the limit of very small amplitudes. Finally, we briefly describe self-similar and shock wave solutions of that equation.
We investigate a mechanical system consisting of infinite number of harmonically coupled pendulums which can impact on two rigid rods. Because of gravitational force the system has two degenerate ground states. The related topological kink - likely the simplest one presented in literature so far - is a compacton, that is it has strictly finite extension. In the present paper we elucidate the relation of such system with sine-Gordon model. Also, solutions describing waves with large amplitude, and an asymptotic formula for the width of the kink are obtained.