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Vortex knots in a Bose-Einstein condensate

Wednesday 5th December 2012 - 12:20 to 12:35
INI Seminar Room 1
Session Title: 
Knots in mathematics: Knot energies
Session Chair: 
Jason Cantarella
I will present a method for numerically building a quantum vortex knot state in the single scalar field wave function of a Bose-Einstein condensate. I will show how the two topologically simplest vortex knots wrapped over a torus evolve and may preserve their shapes by reporting results of the integration in time of the governing Gross-Pitaevskii equation.

In particular, I will focus on how the velocity of a vortex knot depends on the ratio of poloidal and toroidal radius: in a first approximation it is linear and, for smaller ratio, the knot travels faster. Finally, I will display mechanisms of vortex breaking by reconnections which produce simpler vortex rings whose number depends on initial knot topology.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons