EPSRC Reference: 
EP/G009678/1 
Title: 
Knot solitons in superconductors? A definitive test of the BabaevFaddeevNiemi hypothesis 
Principal Investigator: 
Speight, Professor JM 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Pure Mathematics 
Organisation: 
University of Leeds 
Scheme: 
Standard Research 
Starts: 
30 June 2009 
Ends: 
26 December 2012 
Value (£): 
217,841

EPSRC Research Topic Classifications: 
Condensed Matter Physics 
Mathematical Physics 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 
Panel Date  Panel Name  Outcome 
04 Sep 2008

Mathematics Prioritisation Panel

Announced


Summary on Grant Application Form 
Superconductivity occurs when the charged particles which conduct electricity (usually electrons) pair off with one another and start to behave rather like a fluid. In some superconductors, this pairing can occur in more than one way, and one has more than one such fluid coexisting in the material. This situation is described mathematically by multicomponent GinzburgLandau theory. In recent years, it has been realized that the presence of the extra fluid(s) can lead to astonishing and entirely unexpected new effects.By means of an ingenious, but rather controversial, mathematical argument, theoretical physicists Babaev, Faddeev and Niemi have argued that twocomponent GinzburgLandau theory can be reduced to an ostensibly entirely unrelated mathematical model called the FaddeevSkyrme model. This would be extremely exciting, since the FaddeevSkyrme model is known to possess socalled knot solitons: stable, localized lumps of energy which cannot dissipate since the field variable in which they reside is knotted in space. Quite apart from their intrinsic mathematical interest, the appearance of such knot solitons is unprecedented in condensed matter physics.The principal aim of the proposed reasearch is to answer definitively whether the BabaevFaddeevNiemi hypothesis is correct. The crux of their argument is to observe that when the direct coupling between certain of the fields in the twocomponent GinzburgLandau model is neglected (or turned off ) the model reduces to the FaddeevSkyrme model. We will test this claim directly by simulating the behaviour of the GinzburgLandau model as the couplings are slowly turned back on. This will require large scale computer simulations on the White Rose parallel computation grid.

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Organisation Website: 
http://www.leeds.ac.uk 