Vortices in Bose-Einstein Condensates
File(s)
Author(s)
Alex-Duduyemi, Omofolarin
Type
Thesis
Abstract
This thesis surveys aspects of the very broad topic of vortex dynamics in Bose-Einstein condensates. The Gross-Pitaevskii equation (GPE) is an important and popular tool in this regard, and we discuss a number of its properties which are relevant to the study of vortex dynamics. Using the GPE, we explore the dynamics of point vortices in Bose-Einstein condensates, writing hydrodynamic relations we have not encountered elsewhere in the literature. For incompressible condensates, we pay particular attention to discussions of the structure of the Hamiltonian system, and we revisit the topic of linear stability analysis for a steadily rotating, regular polygon of vortices. Furthermore, geometric mechanics is a powerful tool in the study of fluid dynamics, and we make use of the language of geometric mechanics, in particular the Lie derivative, to gain insights into some of the consequences of describing superfluid dynamics using the GPE. We have not encountered the relations we have derived as a result of this effort elsewhere in the
literature. The topics of vortex formation, general approaches to describing vortex dynamics and phonon emission are also discussed.
literature. The topics of vortex formation, general approaches to describing vortex dynamics and phonon emission are also discussed.
Version
Open Access
Date Issued
2019-10
Date Awarded
2021-03
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
Advisor
Jensen, Henrik
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Masters
Qualification Name
Master of Philosophy (MPhil)