000			03869nam a22005295i 4500
001			978-0-8176-4492-5
003			DE-He213
005			20251006084435.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780817644925
020			_a99780817644925
024	7		_a10.1007/0-8176-4492-X _2doi
082	0	4	_a515.353 _223
100	1		_aAftalion, Amandine. _eauthor.
245	1	0	_aVortices in Bose-Einstein Condensates _h[electronic resource] / _cby Amandine Aftalion.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2006.
300			_aXII, 203 p. 18 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProgress in Nonlinear Differential Equations and Their Applications ; _v67
505	0		_aThe 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.
520			_aSince 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.
650		0	_aMATHEMATICS.
650		0	_aDIFFERENTIAL EQUATIONS, PARTIAL.
650		0	_aMATHEMATICAL PHYSICS.
650		0	_aTHERMODYNAMICS.
650		0	_aCONDENSED MATTER.
650		0	_aSUPERCONDUCTIVITY.
650	1	4	_aMATHEMATICS.
650	2	4	_aPARTIAL DIFFERENTIAL EQUATIONS.
650	2	4	_aSUPERCONDUCTIVITY, SUPERFLUIDITY, QUANTUM FLUIDS.
650	2	4	_aMATHEMATICAL METHODS IN PHYSICS.
650	2	4	_aCONDENSED MATTER.
650	2	4	_aMECHANICS, FLUIDS, THERMODYNAMICS.
650	2	4	_aAPPLICATIONS OF MATHEMATICS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817643928
830		0	_aProgress in Nonlinear Differential Equations and Their Applications ; _v67
856	4	0	_uhttp://dx.doi.org/10.1007/0-8176-4492-X _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59670 _d59670