Vortices in Bose-Einstein condensates
Since the first experimental achievement of Bose Einstein condensates (BEC) in 1995 and the award of the Nobel Prize for Physics in 2001, the properties of these gaseous quantum fluids have been the focus of international interest in physics. This monograph is dedicated to the mathematical modelling...
Gorde:
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| Formatua: | Livre numérique |
| Hizkuntza: | Anglais |
| Argitaratua: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Edizioa: | 1st ed. 2006. |
| Saila: | Progress in Nonlinear Differential Equations and Their Applications
67 |
| Gaiak: | |
| Sarrera elektronikoa: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Oharra: |
Description d'après consultation du 02 mai 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Vortices in Bose-Einstein condensates, Amandine Aftalion, 2006, Boston, Birkhäuser, 1 vol. (XII-203 p.), Progress in nonlinear differential equations and their applications, 0-8176-4392-3 • Vortices in Bose-Einstein Condensates, Texte imprimé, 9780817671013 • Vortices in Bose-Einstein condensates, Amandine Aftalion, 2006, Boston, Birkhäuser, 1 vol. (XII-203 p.), Progress in nonlinear differential equations and their applications, 0-8176-4392-3 |
| Gaia: | Since the first experimental achievement of Bose Einstein condensates (BEC) in 1995 and the award of the Nobel Prize for Physics in 2001, the properties of these gaseous quantum fluids have been the focus of international interest in physics. This monograph is dedicated to the mathematical modelling of some specific experiments which display vortices and to a rigorous analysis of features emerging experimentally. In contrast to a classical fluid, a quantum fluid such as a Bose Einstein condensate can rotate only through the nucleation of quantized vortices beyond some critical velocity. There are two interesting regimes: one close to the critical velocity, where there is only one vortex that has a very special shape; and another one at high rotation values, for which a dense lattice is observed. One of the key features related to superfluidity is the existence of these vortices. We address this issue mathematically and derive information on their shape, number, and location. In the dilute limit of these experiments, the condensate is well described by a mean field theory and a macroscopic wave function solving the so-called Gross Pitaevskii equation. The mathematical tools employed are energy estimates, Gamma convergence, and homogenization techniques. We prove existence of solutions that have properties consistent with the experimental observations. Open problems related to recent experiments are presented. The work can serve as a reference for mathematical researchers and theoretical physicists interested in superfluidity and quantum fluids, and can also complement a graduate seminar in elliptic PDEs or modelling of physical experiments |
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| Alearen deskribapena: | Description d'après consultation du 02 mai 2011 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. p. [199]-203. Index |
| ISBN: | 9780817644925 |
| ISSN: | 2374-0280 |
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