TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Vortices in BoseEinstein Condensates
T2  - Progress in Nonlinear Differential Equations and Their Applications
SN  - 9780817644925
AV  - QA370-380 
U1  - 515.353 23
PY  - 2006///
CY  - Boston, MA
PB  - Birkhuser Boston
KW  - Mathematics
KW  - Differential equations, partial
KW  - Mathematical physics
KW  - Thermodynamics
KW  - Condensed matter
KW  - Superconductivity
KW  - Partial Differential Equations
KW  - Superconductivity, Superfluidity, Quantum Fluids
KW  - Mathematical Methods in Physics
KW  - Condensed Matter
KW  - Mechanics, Fluids, Thermodynamics
KW  - Applications of Mathematics
N1  - 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; ZDB-2-SMA
N2  - Since the first experimental achievement of BoseEinstein 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 BoseEinstein 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 GrossPitaevskii 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
UR  - http://dx.doi.org/10.1007/0-8176-4492-X
ER  -