Amandine Aftalion

Vortices in Bose-Einstein Condensates (eBook, PDF)

• Format: PDF

Produktbeschreibung

One of the key issues related to superfluidity is the existence of vortices. In very recent experiments on Bose–Einstein condensates, vortices have been observed by rotating the trap holding the atoms. In contrast to a classical fluid for which the equilibrium velocity corresponds to solid body rotation, a quantum fluid such as a Bose–Einstein condensate can rotate only through the nucleation of quantized vortices. This monograph is dedicated to the mathematical modelling of these phenomena.

The mathematical tools employed are energy estimates, Gamma convergence, and homogenization techniques. The mathematical analysis is made in the framework of the Gross–Pitaevskii energy. Results are presented and open problems related to recent experiments are explained.

The work can serve as a reference for mathematical researchers and theoretical physicists interested in superfluidity and quantum condensates, and can also complement a graduate seminar in elliptic PDEs or modelling of physical experiments.

Produktdetails

• Verlag: Birkhäuser Boston
• Erscheinungstermin: 14. Oktober 2007
• Englisch
• ISBN-13: 9780817644925
• Artikelnr.: 37355645

Inhaltsangabe

The Physical Experiment and Their Mathematical Modeling.- The Mathematical Setting: A Survey of the Main Theorems.- Two-Dimensional Model for otating Condensate.- Other Trapping Potentials.- High-Velocity and Quantam Hall Regime.- Three-Dimensional Rotating Condensate.- Superfluid Flow Around an Obstacle.- Further Open Problems.

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Preface.- The Physical Experiments and Their Mathematical Modelling.- The Mathematical Setting: A Survey of the Main Theorems.- Two-dimensional Model for a Rotating Condensate.- Other Trapping Potentials.- High Velocity and Quantum Hall Regime.- Three-dimensional Rotating Condensate.- Superfluid Flow around an Obstacle.- Further Open Problems.- References.- Index.

Rezensionen

"The book is a compilation of several recent papers in the rigorous analysis of the Gross-Pitaevski\u\i functional in various physically relevant regimes, as well as a helpful discussion of the physical literature and numerical studies of vortices in BEC. Most of the analysis is done for the Thomas-Fermi limit in two-dimensional cases." -- MathSciNet

"This monograph by Amandine Aftalion presents rigorous mathematical models of some experiments on BECs which display vortices." -- Zetralblatt Math