Chapter

Vortices in Bose—Einstein Condensates

Volume 67 of the series Progress in Nonlinear Differential Equations and Their Applications pp 1-17

The Physical Experiment and Their Mathematical Modeling

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Abstract

Bose-Einstein condensation (BEC), first predicted by Einstein in 1925, has been realized experimentally in 1995 in alkali gases. The award of the 2001 Nobel Prize in Physics to E. Cornell, C. Wieman, and W. Ketterle acknowledged the importance of the achievement. In this new state of matter, which is very dilute and at very low temperature, a macroscopic fraction of the atoms occupy the same quantum level, and behave as a coherent matter wave similar to the coherent light wave produced by a laser. In the dilute limit, the condensate is well described by a mean-field theory and a macroscopic wave function. The properties of these gaseous quantum fluids have been the focus of international interest in physics, both experimentally and theoretically, and many applications are envisioned. An important issue is the relationship between BEC and superfluidity, in particular through the existence of vortices. The focus of this book is the mathematical properties of vortices, observed in very recent experiments on rotating condensates