|
|
0000-0002-7923-5739
| Home | Research | Talks | Students | Teaching | CV | GMoM |
Topological solitons are a beautiful class of object that are discrete particle like solutions of continous field theories that appear at every scale of the physical world. They appear as finite energy, localised solutions of nonlinear wave equations, whose stability arise from the topological nature of the constituent fields. They have a variety of applications in several areas including particle physics, cosmology and condensed matter physics. Below are some examples of the topological solitons I'm particularly interested in:
When a magnetic field is applied to a superconductor it penetrates at discrete points around which a fluid of superconducting electrons circulate. These vortices form triangular lattices of increasing density as the applied field is increased.
Current interest is focussed on multi-component materials, where electrons pair over multiple fermi surfaces, such that vortices are formed of multiple fractional vortices. We have shown that such materials exhibit vortices that break the ussual symmetries and thus interact in un-intuitive ways:
Skyrmions are 3-dimensional solitons that act as an effecitive model of nuclei, where the number of solitons corresponds to the baryon number N (number of protons and neutrons). Most effective models of nuclei require many parameters to fit to data, where as miracously the Skyrme model matches data with just two! with multi-soliton configurations exhibiting striking geometric symmetries. The multi-soliton (N>1) configurations exhibit strikingly symmetric bound states or confgurations, similar to polyhedra. However, quantising an infinite dimensional configuration space is implausable and thus my current work focusses on constructing and quantising over finite-dimensional subspaces that approximate the low-energy dynamics. We recently proposed that the natural sub-space is 8N-dimensional and can be directly constructed from the space of Yang-Mills instantons:
For higher baryon number there are often multiple symmetric critical points or configurations that are not degenerate and should all be quantised over. Thus we have proposed that the configuration space should be approximated as a graph of steepest decent curves between symmetric critical points, defining a quantum graph:
In chiral magnets the direction of spins naturally exhibit twists. This leads to tubes of localised twists spointaneously forming. We call the 2-dimensional cross-section of these tubes a magnetic kyrmion or baby skyrmion as it acts like a 2-dimensnional analogue of 3-dimensional skyrmions.
We also studied the model with di-hedral symmetry in the potential as a toy model for nuclei formed of discrete partons hsowing the solutions form polyforms, planar figures formed by regular N-gons joined along their edges:
Cosmic strings are proposed to form during phase tranitions in the early universe, they are modelled as vortices in scalar fields called the Abelian Higgs model (similar to the votices in superconuductors). There is a lot of interest in understanding how energetic networks of these strings evolve so as to detect them. To understand this we need to understand the dynamics of the vortices that form them. As they are highly energetic objects study the scattering of the strings when their modes are excited:
Monopoles are solitons in Yang-Mills-Higgs gauge theories that carry magnetic charge. Importantly, the static model is integrable, however their dynamics are not. Much of the focus is on the low-energy dynamics which we model as geodesic motion on a moduli space of static solutions.
|
|
|
|