Abstract |
In the present work we discuss non-linear physics problems such as Nielsen-
Olesen strings, superconducting bosonic straight strings and static vortex
rings. We start with a toy model. We search for antiperiodic solitons of the
Goldstone model on a circle. Such models provide the basis as well as useful
hints for further research on three-dimensional more realistic problems. We
proceed with a full research on a U(1) model which admits stable straight
string solutions in a small, numerically determined area. That model has a
Ginzburg-Landau potential with a cubic term added to it and can be found
in condensed matter problems as well. The next part of our research, has
to do with a U(1) × U(1) model which is the main subject of our interest.
There, we search for stable axially symmetric solutions which are solitons,
which can represent particles, the mass of which is of the order of TeV.
The confirmation or rejection of the existence of those defects is of great
interest if we consider that LHC will work in the same energy range. In our
study, we find out that due to current quenching, these vortex rings seem
to be unstable. We also extend the model of vortex rings by adding higher
derivative terms which are favorable for stability. After the extensive analysis
we performed, we conclude that these objects don’t seem to be stable. The
reasons which brought us to this conclusion are explained.
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