Overview
- Dedicated to the mathematical modelling of vortices in Bose–Einstein condensates and related phenomena
- Analysis employs energy estimates, Gamma convergence, and homogenization techniques, in the framework of the Gross–Pitaevskii energy
- Results are presented and open problems explained
- Can serve as a reference on superfluidity and quantum condensates, or a grad seminar in elliptic PDEs or modelling of physical experiments
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 67)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
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
Authors and Affiliations
Bibliographic Information
Book Title: Vortices in Bose-Einstein Condensates
Authors: Amandine Aftalion
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/0-8176-4492-X
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2006
Hardcover ISBN: 978-0-8176-4392-8Published: 06 June 2006
eBook ISBN: 978-0-8176-4492-5Published: 14 October 2007
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XII, 203
Number of Illustrations: 18 b/w illustrations
Topics: Partial Differential Equations, Strongly Correlated Systems, Superconductivity, Mathematical Methods in Physics, Condensed Matter Physics, Classical and Continuum Physics, Applications of Mathematics