Bose-Einstein condensates

Monday, October 31, 2016 - 3:15pm - 4:05pm
Panayotis Kevrekidis (University of Massachusetts)
Motivated by work in nonlinear optics, as well as more recently
in Bose-Einstein condensate mixtures, we will explore a
series of nonlinear states that arise in such systems. We
will start from a single structure, the so-called dark-bright solitary wave, and then
expand our considerations to multiple such waves, their
spectral properties, nonlinear interactions and experimental
observations. A twist will be to consider the dark
solitons of the one component as effective potentials that will trap the bright
Monday, October 31, 2016 - 11:30am - 12:20pm
Thomas Chen (The University of Texas at Austin)
The Hartree and the nonlinear Schrodinger equation can be derived as the mean field limit of the dynamics of an interacting gas of Bosons exhibiting Bose-Einstein condensation; the nonlinear dispersive PDE describes the dynamics of the Bose-Einstein condensate. The topic of this talk is an extension to the Hartree equation, which describes thermal fluctuations around the Bose-Einstein condensate. Using quasifree reduction, we derive the Hartree-Fock-Bogoliubov (HFB) equations, and discuss the well-posedness of the corresponding Cauchy problem.
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