Alberto Enciso (ICMAT, Spain)

PDL C38
Abstract: The GrossPitaevskii equation is a nonlinear Schrödinger
equation that models the behavior of a BoseEinstein condensate. The
quantum vortices of the condensate are defined by the zero set of the
wave function at time $t$. In this talk we will present recent work
about how these quantum vortices can break and reconnect in
arbitrarily complicated ways. As observed in the physics literature,
the distance between the vortices near the breakdown time, say t=0,
scales like the square root of t: it is the socalled $t^{1/2}$ law.
At the heart of the proof lies a remarkable global approximation
property for the linear Schrödinger equation. The talk is based on
joint work with Daniel PeraltaSalas.