Soliton Scattering on Obstructions in Relativistic Theories

We present results of our studies of various scattering properties of topological and non-topological solitons on obstructions in the form of holes and barriers in (1+1) and (2+1) dimensions. These obstructions, barriers and holes, are inserted into the potential of the theory via the coupling parameter, ${\it ie}$ $\tilde\lambda$, that is effective only in a certain region of space. When $\tilde\lambda>1$ the obstruction is a barrier and when $0<\tilde\lambda<1$ the obstruction is a hole. Our results are based on numerical simulations and analytical considerations for a variety of models. First, we discuss the scattering properties of two models involving a \varphi⁴ potential. In the first model the potential parameter is included in the potential and in the second model the potential parameter is included in the metric. Second, we study various scattering properties of topological solitons in two classes of models, which are the generalisations of the Sine-Gordon model and which have recently been proposed by Bazeia et al. These two classes of models depend on a positive real non-zero parameter $n$ but in this paper we consider the models only for its integer values as when $n=2$ (for the first class) and $n=1$ (for the second class), the model reduce to the Sine-Gordon one. We take the soliton solutions of these models (generalisations of the `kink' solution of the Sine-Gordon model) and consider their scattering on potential holes and barriers. We present our results for $n=1,...6$. We find that, like in the Sine-Gordon models, the scattering on the barrier is very elastic while the scattering on the hole is inelastic and can, at times, lead to a reflection. We discuss the dependence of our results on $n$ and find that the critical velocity for the transmission through the hole is lowest for $n=3$. Next, we discuss various scattering properties of non-topological solitons, Q-balls, on potential obstructions in $\left(1+1\right)$ and $\left(2+1\right)$ dimensions. The dynamics of Q-balls on such obstructions in $\left(1+1\right)$ dimensions is shown to be very similar to that of topological solitons provided that the Q-balls are stable. In $\left(2+1\right)$ dimensions, numerical simulations have shown some differences from the dynamics of topological solitons. We discuss these differences in some detail. Next, we approach the dynamics of various soliton-obstruction systems from analytical perspective and compare the analytical results with the ones observed in numerical simulations. Finally, we show that a realisation of spectral flow as a coordinate transformation for asymptotically four-dimensional solutions can be extended to the non-supersymmetric case. We apply this transformation to smooth geometries describing microstates of the D1-D5-KK monopole system in type IIB supergravity compactified on a six-torus, and obtain solutions with an additional momentum charge. We study the supersymmetric and near-core limits of this construction.

Name dc:type.qualificationname

PhD

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

Durham University

Year dc:date.issued

2010

Author dc:creator

• al-Alawi, Jassem Hassan