arXiv subjects
Publications and source records attributed to W. J. Zakrzewski.
Recently we have presented in hep-th/9811071 an ansatz which allows us to construct skyrmion fields from the harmonic maps of $S\sp2$ to $CP\sp{N-1}$. In this paper we examine this construction in detail and use it to construct, in an explicit form, new static spherically symmetric solutions of the SU(N) Skyrme models. We also discuss some properties of these solutions.
Static properties of multiskyrmions with baryon numbers up to 8 are calculated starting from recently given rational map ansaetze. The spectra of baryonic systems with strangeness, charm and bottom are estimated within a "rigid oscillator" version of the bound state soliton model. It is suggested that the recently observed negatively charged nuclear fragment can be considered as quantized strange multiskyrmion with baryon number 6 or 7 and large value of strangeness. In agreement with previous observation, it is argued that baryonic systems with charm or bottom quantum numbers have more chances to be bound with respect to strong interactions than strange baryonic systems.
We show that any solution of the SU(2) Skyrme model can be used to give a topologically trivial solution of the SU(4) one. In addition, we extend the method introduced by Houghton et al. and use harmonic maps from S2 to CP(N-1) to construct low energy configurations of the SU(N) Skyrme models. We show that one of such maps gives an exact, topologically trivial, solution of the SU(3) model. We study various properties of these maps and show that, in general, their energies are only marginally higher than the energies of the corresponding SU(2) embeddings. Moreover, we show that the baryon (and energy) densities of the SU(3) configurations with baryon number B=2-4 are more symmetrical than their SU(2) analogues. We also present the baryon densities for the B=5 and B=6 configurations and discuss their symmetries.
Due to a computational mistake this paper has been withdrawn.
Due to a computational mistake this paper has been withdrawn.
The $CP^2$ model, with and without a generalized Hopf term, is studied using the collective coordinate approximation. In the spirit of this approximation, an ansatz is given which in previous numerical studies was seen to give a good parameterization of the numerical solution. The equations of motion for the collective coordinates are then solved analytically, for solitons close together and for solitons far apart. The solutions show how the generalized Hopf term changes the scattering angle which in its absence is $90^{\circ}$.
We study the 3+1 dimensional Skyrme model with a mass term different from the usual one. We show that this new model possesses domain walls solutions. We describe how, in the equivalent 2+1 dimensional model, the Skyrmion is absorbed by the wall.
We report our observations that the baby-Skyrme model in (2+1) dimensions possesses non-topological stationary solutions which we call pseudo-breathers. We discuss their properties and present our results on their interaction with the topological skyrmions.
We study classical solutions of the vector O(3) sigma model in (2+1) dimensions, spontaneously broken to O(2)xZ2. The model possesses Skyrmion-type solutions as well as stable domain walls which connect different vacua. We show that different types of waves can propagate on the wall, including waves carrying a topological charge. The domain wall can also absorb Skyrmions and, under appropriate initial conditions, it is possible to emit a Skyrmion from the wall.
Using numerical simulations, the stability and scattering properties of the O(3) model on a two-dimensional torus are studied. Its solitons are found to be unstable but can be stabilized by the addition of a Skyrme term to the Lagrangian. Scattering at right angles with respect to the initial direction of motion is observed in all cases considered. The model has no solutions of degree one, so when a field configuration that resembles a soliton is considered, it shrinks to become infinitely thin. A comparison of these results with those of the model defined on the sphere is made.
We use the methods of group theory to reduce the equations of motion of two spin systems in (2+1) dimensions to sets of coupled ordinary differential equations. We present solutions of some classes of these sets and discuss their physical significance.
We study various classical solutions of the baby-Skyrmion model in $(2+1)$ dimensions. We point out the existence of higher energy states interpret them as resonances of Skyrmions and anti-Skyrmions and study their decays. Most of the discussion involves a highly exited Skyrmion-like state with winding number one which decays into an ordinary Skyrmion and a Skyrmion-anti-Skyrmion pair. We also study wave-like solutions of the model and show that some of such solutions can be constructed from the solutions of the sine-Gordon equation. We also show that the baby-Skyrmion has non-topological stationary solutions. We study their interactions with Skyrmions.
We demonstrate the existence of stable time dependent solutions of the Landau-Lifshitz model with a constant external magnetic field. We find such solutions in all topological sectors, including N=0. We discuss some of their properties.
We use the methods of group theory to reduce the equations of motion of the $CP^{1}$ model in (2+1) dimensions to sets of two coupled ordinary differential equations. We decouple and solve many of these equations in terms of elementary functions, elliptic functions and Painlev{é} transcendents. Some of the reduced equations do not have the Painlev{é} property thus indicating that the model is not integrable, while it still posesses many properties of integrable systems (such as stable ``numerical'' solitons).
In the spirit of previous papers, but using more general field configurations, the non-linear O(3) model in (2+1)-D, modified by the addition of both a potential-like term and a Skyrme-like term, is considered. The instanton solutions are numerically evolved in time and some of their stability properties studied. They are found to be stable, and a repulsive force is seen to exist among them. These results, which are restricted to the case of zero speed systems, confirm those obtained in previous investigations, in which a similar problem was studied for a different choice of the potential-like term.
Baby Skyrmions are topological solitons in a (2+1)-dimensional field theory which resembles the Skyrme model in important respects. We apply some of the techniques and approximations commonly used in discussions of the Skyrme model to the dynamics of baby Skyrmions and directly test them against numerical simulations. Specifically we study the effect of spin on the shape of a single baby Skyrmion, the dependence of the forces between two baby Skyrmions on the baby Skyrmions' relative orientation and the forces between two baby Skyrmions when one of them is spinning.
We modify the recently proposed model of Speight and Ward to make it possess time dependent solutions. We find that for each lattice spacing and for each velocity of the sine Gordon kink we can find a modification of the model for which this kink is a solution. We find that this model has really 3 ``kink-like" solutions; the original kink, the static kink and a further kink moving with velocity $v\sim0.97$. We discuss various properties of the model, from the point of view of its usefulness for numerical simulations.
The Skyrme model can be generalised to a situation where static fields are maps from one Riemannian manifold to another. Here we study a Skyrme model where physical space is two-dimensional euclidean space and the target space is the two-sphere with its standard metric. The model has topological soliton solutions which are exponentially localised. We describe a superposition procedure for solitons in our model and derive an expression for the interaction potential of two solitons which only involves the solitons' asymptotic fields. If the solitons have topological degree 1 or 2 there are simple formulae for their interaction potentials which we use to prove the existence of solitons of higher degree. We explicitly compute the fields and energy distributions for solitons of degrees between one and six and discuss their geometrical shapes and binding energies.