arXiv subjects

R. S. Ward

Publications and source records attributed to R. S. Ward.

31 records · Page 2Linked to original sources

arXiv2004

Planar Skyrmions at high and low density

The O(3) Skyrme system in two space dimensions admits topological soliton solutions. This paper studies the transition between the high-density crystalline phase of such solitons and the low-density phase where there are multi-Skyrmions localized in space. The details depend crucially on the choice of the potential function. Two such choices are investigated: in the first system, multi-Skyrmions at low density form a ring; while in the second, there is an explicit crystal solution, and the preferred low-density configurations are chunks of this crystal. The second system is a particularly good analogue of three-dimensional Skyrmions.

hep-th↗

arXiv2003

Topological Q-Solitons

Static topologically-nontrivial configurations in sigma-models, for spatial dimension D \geq 2, are unstable. The question addressed here is whether such sigma-model solitons can be stabilized by steady rotation in internal space; that is, rotation in a global SO(2) symmetry. This is the mechanism which stabilizes Q-balls (non-topological solitons). The conclusion is that the Q-mechanism can stabilize topological solitons in D=2 spatial dimensions, but not for D=3.

hep-th↗

arXiv2002

Stability of Sigma-Model Strings and Textures

In flat space-time, sigma-model strings and textures are both unstable to collapse and subsequent decay. With sufficient cosmological expansion, however, they are stable in a generalized sense: a small perturbation will cause them to change their shape, but they do not decay. The current rate of expansion is sufficient to stabilize strings, but not textures.

gr-qc↗

arXiv2001

Hopf Solitons from Instanton Holonomy

The holonomy of an SU(2) N-instanton in the x^4-direction gives a map from R^3 into SU(2), which provides a good model of an N-Skyrmion. Combining this map with the standard Hopf map from SU(2)=S^3 to S^2 gives a configuration for a Hopf soliton of charge N. In this way, one may define a collective-coordinate manifold for Hopf solitons. This paper deals with instanton approximations to Hopf solitons in the Skyrme-Faddeev model, focussing in particular on the N=1 and N=2 sectors, and the two-soliton interaction.

hep-th↗

arXiv2001

Skyrmions on the Two-Sphere

We study static solutions of the Skyrme model on the two-sphere of radius L, for various choices of potential. The high-density Skyrmion phase corresponds to the ratio beta=L/(size of Skyrmion) being small, whereas the low-density phase corresponds to beta being large. The transition between these two phases, and in particular the behaviour of a relevant order parameter, is examined.

hep-th↗

arXiv2000

The Interaction of Two Hopf Solitons

This Letter deals with topological solitons in an O(3) sigma model in three space dimensions (with a Skyrme term to stabilize their size). The solitons are classified topologically by their Hopf number N. The N=2 sector is studied; in particular, for two solitons far apart, there are three ``attractive channels''. Viewing the solitons as dipole pairs enables one to predict the force between them. Relaxing in the attractive channels leads to various static 2-soliton solutions.

hep-th↗

arXiv1999

Kink dynamics in a novel discrete sine-Gordon system

A spatially-discrete sine-Gordon system with some novel features is described. There is a topological or Bogomol'nyi lower bound on the energy of a kink, and an explicit static kink which saturates this bound. There is no Peierls potential barrier, and consequently the motion of a kink is simpler, especially at low speeds. At higher speeds, it radiates and slows down.

patt-sol↗

arXiv1998

Lax Pairs for Integrable Lattice Systems

This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes the features that are needed to obtain equations which are local on the spatial lattice.

solv-int↗

arXiv1996

Bogomol'nyi Bounds for Two-Dimensional Lattice Systems

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 is that instantons/solitons/vortices on the lattice then have a high degree of stability.

hep-th↗

arXiv1995

Conserved quantities for integrable chiral equations in 2+1 dimensions

The integrable (2+1)-dimensional chiral equations are related to the self-dual Yang-Mills equation. Previously-known nonlocal conservation laws do not yield finite conserved charges, because the relevant spatial integrals diverge. We exhibit infinite sequences of conserved quantities that do exist, and have a simple explicit form.

solv-int↗

arXiv1995

Nontrivial scattering of localized solitons in a (2+1)-dimensional integrable system

One usually expects localized solitons in integrable systems to interact trivially. There is an integrable (2+1)-dimensional chiral equation which admits multi-soliton solutions with trivial dynamics. This paper describes how to generate explicit solutions representing nontrivial soliton interactions: in particular, a head-on collision of two solitons resulting in $90^\circ$ scattering.

solv-int↗

arXiv1995

Discrete Toda Field Equations

There are two-dimensional Toda field equations corresponding to each (finite or affine) Lie algebra. The question addressed in this note is whether there exist integrable discrete versions of these. It is shown that for certain algebras (such as $A_n$, $A_n^{(1)}$ and $B_n$) there do, but some of these systems are defined on the half-plane rather than the full two-dimensional lattice.

solv-int↗

arXiv1995

Stable Topological Skyrmions on the 2D Lattice

In the continuum O(3) sigma model in two spatial dimensions, there are topological solitons whose size can be stabilized by adding Skyrme and potential terms. This paper describes a lattice version, namely a natural way of modifying the 2d Heisenberg model to achieve topological stability on the lattice.

hep-th↗