Quantum Topology / Hopf Algebra Seminar

Daniel Peralta-Salas
Instituto de Ciencias Matematicas (ICMAT), Madrid
Seifert surfaces and existence of vortex reconnections in quantum fluids.
Abstract: The quantum vortices of a superfluid are described as nodal lines of a solution to the time-dependent Gross-Pitaevskii equation. Experiments in Lab and extensive numerical computations show that quantum vortices cross, each of them breaking into two parts and exchanging part of itself for part of the other. This phenomenon, known as quantum vortex reconnection, occurs even though the superfluid does not lose its smoothness. This usually leads to a change of topology of the quantum vortices. In this talk I will show that, given any initial and final congurations of quantum vortices (i.e. closed curves, possibly knotted and linked), and any way of transforming one into the other through a generic Seifert surface embedded in spacetime, there is an initial condition whose associated solution realizes this specific vortex reconnection scenario. This allows us to track the vortex reconnection process at all times, both locally and globally. Moreover, just as in the physics literature, the distance between vortices near the reconnection time obeys the so called t^{1/2} law. This is based on joint work with Alberto Enciso.
Tuesday February 26, 2019 at 2:00 PM in 427 SEO
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