A study of dynamical vortices in the Abelian-Higgs and Chern-Simons models
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Abstract
Vortices are common to many physical systems. Most people, for example,
are familiar with eddies that form in streams and rivers. They usually have an
energy density per unit length which is "localized" and, consequently, their crosssections
may be thought of as "particles" in two dimensions. Theories which support
stable vortex solutions are highly non-linear; and therefore, their study has relied
heavily upon computer simulations. In this dissertation, I numerically explore the
dynamical interactions of vortices in the (3 + 1) Abelian Higgs and (2 + 1) ChernSimons
theories. Both of these models involve a complex scalar field coupled to a
U (l) gauge field.
I present the results of computer simulations which involve parallel vortices
and anti-vortices for a wide range of parameters. For example, I show that when
critically-coupled vortices collide, the scattering results are approximately velocity
independent until β ∼ 0.3 and the collisions are approximately elastic until β ∼ 0.3.
This implies that the higher-order modes, which can in general be excited from a
collision, "decouple" from the dynamics when β ≤ 0.3. I use these results to study
the metric on the moduli space M_2, calculating the metric from its field-kinetic
definition. The scattering angles, calculated directly from the metric components,
are shown to agree with the numerical simulations. The non-trivial form of the
components are discussed in relation to the scattering results. I also discuss vortices
as to their application to cosmology and numerically study a cosmic string loop
collapsing under its own tension.
I also study the dynamics of non-topological vortices in the (2 + 1) nonlinear
gauged Schroedinger equation. For several parameters, I perform simulations of two
colliding vortices, finding the scattering to be peaked in the forward direction after
a vortex/vortex head-on collision. I also find that the vortices do not retain their
radially symmetric shape after the collision. This suggests that the vortices are
not solitons and that the collisions are inelastic. Moreover, the scattering results
for collisions with non-zero impact parameters b are not symmetrical under the
reflection b → −b.
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This work is being made available in OpenBU by permission of its author, and is available for research purposes only. All rights are reserved to the author.