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In mathematics and physics, solitons, topological solitons and topological defects are three closely related ideas, all of which signify structures in a physical system that are stable against perturbations. Solitons won't decay, dissipate, disperse or evaporate in the way that ordinary waves might. The stability arises from an obstruction to the decay, which is explained by having the soliton belong to a different topological homotopy class or cohomology class than the base physical system. More simply: it is not possible to continuously transform the system with a soliton in it, to one without it. The mathematics behind topological stability is both deep and broad, and a vast variety of systems possessing topological stability have been described. This makes categorization somewhat difficult.
In particle theory, the skyrmion is a topologically stable field configuration of a certain class of non-linear sigma models. It was originally proposed as a model of the nucleon by Tony Skyrme in 1961. As a topological soliton in the pion field, it has the remarkable property of being able to model, with reasonable accuracy, multiple low-energy properties of the nucleon, simply by fixing the nucleon radius. It has since found application in solid-state physics, as well as having ties to certain areas of string theory.
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There should be two "dual equivalent" field formulations of the same theory in which electric (Noether) and magnetic (topological) quantum numbers exchange roles.
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In physics, magnetic skyrmions are statically stable solitons which have been predicted theoretically and observed experimentally in condensed matter systems. Magnetic skyrmions can be formed in magnetic materials in their 'bulk' such as in manganese monosilicide (MnSi), or in magnetic thin films. They can be achiral, or chiral in nature, and may exist both as dynamic excitations or stable or metastable states. Although the broad lines defining magnetic skyrmions have been established de facto, there exist a variety of interpretations with subtle differences.
John Clayton Taylor is a British mathematical physicist. He is an Emeritus Professor of Mathematical Physics at the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge and an Emeritus Fellow of Robinson College. He is the father of mathematician Richard Taylor.
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References
- 1 2 Nicholas Manton at the Mathematics Genealogy Project
- ↑ Autobiographical Memoir, p.7
- 1 2 3 "Nicholas Manton". London: Royal Society. One or more of the preceding sentences may incorporate text from the royalsociety.org website where "all text published under the heading 'Biography' on Fellow profile pages is available under Creative Commons Attribution 4.0 International License." "Royal Society Terms, conditions and policies". Archived from the original on 20 February 2016. Retrieved 9 March 2016.
{{cite web}}: CS1 maint: bot: original URL status unknown (link) - ↑ Professor Nicholas Manton, University of Cambridge, retrieved 2016-03-10.
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