Bose-Einstein Condensates : Theory, Characteristics, and Current Research.

Intro -- BOSE EINSTEIN CONDENSATES: THEORY, CHARACTERISTICS AND CURRENT RESEARCH -- BOSE EINSTEIN CONDENSATES: THEORY, CHARACTERISTICS AND CURRENT RESEARCH -- LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA -- CONTENTS -- PREFACE -- Chapter1NEWAPPROACHTOSPINORBOSE-EINSTEINCONDENSATES -- Abstract -- 1.Introduction -- 2.GeneralFormalismfortheSpinDynamics -- 2.1.Overview -- 2.2.SpinRepresentationsofaQuantum2-StatesSystem -- 2.3.TheCanonicalVariables -- 2.4.AConsequenceoftheEhrenfestTheorem -- 3.SpinDynamicsofthe2-statesBose-EinsteinCondensate -- 3.1.BasicEquations -- 3.2.TheZero-TemperatureCase:DeterministicBehavior -- 3.2.1.ConstantMagneticFieldalonganAxisPerpendiculartothez-Direction -- 3.2.2.TheRotatingTransverseMagneticField -- 3.2.3.TheModulatedTransverseMagneticField -- 3.3.TheFinite-TemperatureCase:StochasticBehavior -- 3.3.1.TheFokker-PlanckEquation -- 3.3.2.DerivationoftheFokker-PlanckEquationUsingtheFunctionalIntegralAp-proach -- 4.SpinDynamicsofaMulti-componentBose-EinsteinConden-sate:TunnelingPhenomena -- 4.1.BasicEquations -- 4.2.TunnelingRate -- 4.3.SpecificExamplesofTunneling -- 4.3.1.Model(I) -- 4.3.2.Model(II) -- 5.Conclusion -- AppendixA -- References -- Chapter2QUANTUMINTERFERENCEINTHETIME-OF-FLIGHTDISTRIBUTIONFORATOMICBOSE-EINSTEINCONDENSATES -- Abstract -- 1.Introduction -- 2.InterferenceintheQuantumTime-of-flightDistributionforBose-EinsteinCondensate -- 2.1.VerticalSetup -- 2.2.HorizontalSetup -- 3.NumericalResultsandDiscussions -- 4.SummaryandConclusion -- Acknowledgments -- References -- Chapter3ONTHEDYNAMICSOFNONCONSERVATIVEBOSE-EINSTEINCONDENSATESINTRAPPEDDILUTEGASES -- Abstract -- 1.NonconservativeBose-EinsteinCondensates -- 2.TheMean-fieldApproach -- 3.TechniquesfortheResolutionofNonlinearSchr¨odingerEquations -- 3.1.TimeIndependentVariationalApproach -- 3.2.TimeDependentVariationalApproach -- 3.3.NumericalMethods.

4.UnharmonicTrappingPotentials -- 5.NonlinearPhenomenainBose-EinsteinCondensates -- 5.1.Liquid-GasPhaseTransitioninNonconservativeBose-EinsteinConden-sates -- 5.2.SpatiotemporalChaosinBose-EinsteinCondensates -- 5.3.AutosolitonsinBose-EinsteinCondensates -- 5.4.CoherentDimerFormationNearFeshbachResonancesinBose-EinsteinCondensates -- 6.StabilityofNonconservativeBose-EinsteinCondensates -- 7.FinalRemarks -- References -- Chapter4ELLIPTICVORTICESINSELF-ATTRACTIVEBOSE-EINSTEINCONDENSATES -- Abstract -- 1.Introduction -- 2.TheModelandNumericalAnalysisfortheVortexSolitons -- 3.Conclusion -- References -- Chapter5CLASSICALELECTRODYNAMICSANALOGYOFTWO-DIMENSIONALBOSE-EINSTEINCONDENSATES -- Abstract -- 1.Introduction -- 2.Two-dimensionalBEC -- 3.MappingontoElectrodynamics -- 4.ConservationofEnergy -- 5.ConservationofAngularMomentum -- 6.VelocityField -- 7.VortexMotion -- 7.1.VortexCoreEffect -- 7.2.VortexMass:CyclotronMotionandRetardationEffect -- 7.2.1.CaseofaHomogeneousSuperfluid -- 7.2.2.VortexMassinaFiniteSuperfluid -- 7.2.3.VortexMotioninaBEC:NumericalSimulation -- 8.Conclusion -- Appendix:CalculationoftheVortexVelocity -- References -- Chapter6MATTERWAVEDARKSOLITONSINOPTICALSUPERLATTICES -- Abstract -- 1.Introduction -- 2.TheModel -- 3.Matter-waveBandGapSpectrumandDarkSolitons -- 4.Peierls-NabarroBarrier -- 5.Conclusions -- References -- Chapter7BRIGHTMATTERWAVESANDSTABLEATOMICMODE-LOCKINGINBOSE-EINSTEINCONDENSATES -- Abstract -- 1.Introduction -- 2.PhysicalConfigurationandGoverningEquations -- 2.1.ModelEquations -- 2.2.SolutionsandStability -- 3.AtomicMode-locking -- 3.1.AttractiveCondensate -- 3.2.RepulsiveCondensate -- 3.3.Self-similarMode-locking -- 4.Conclusion -- Acknowledgments -- References -- Chapter8ONTHEMATHEMATICALDESCRIPTIONOFTHEEFFECTIVEBEHAVIOUROFONE-DIMENSIONALBOSE-EINSTEINCONDENSATESWITHDEFECTS -- Abstract -- 1.PhysicalMotivation.

2.ReviewofPointInteractions -- 3.StationaryNLSwithPointInteractions -- 3.1.RepulsiveNonlinearity -- 3.2.AttractiveNonlinearity -- 3.2.1.δinteraction -- 3.2.2.δ′interaction -- 4.StabilityandInstabilityofStationaryStates -- 4.1.StabilityofSolitaryWavesinthePresenceof Interactions -- 4.2.StabilityinthePresenceof ′Interaction -- 5.ScatteringofSolitonsonPointDefects -- References -- Chapter9EXPERIMENTALOBSERVATIONOFSOMEPHENOMENAINBOSE-EINSTEINCONDENSATES -- Abstract -- 1.UltracoldAtomsandBose-EinsteinCondensatesinaTightConfinement -- 1.1.ExperimentalProcess -- 1.2.TheCriterionsofPhaseTransitionforBECsinaQUICTrap -- 1.3.ParametricExcitationofUltracoldAtomsinaQUICTrap -- 2.ColdAtomsandBose-EinsteinCondensatesPassingthroughaGaussianBeam -- 2.1.TheoreticModel -- 2.2.ExperimentalResults -- 3.PreciseManipulationofColdAtomsandBECsonAtomChips -- 3.1.ExperimentalSetup -- 3.2.GuidingNeutralAtomswithTwoCurrent-CarryingWires -- 3.3.DynamicalSplittingandMergingoftheAtomicCloudonAtomChips -- 3.4.Surface-inducedEvaporativeCooling -- 3.5.ParametricResonanceandCoolingonanAtomChip -- 3.6.Bose-EinsteinCondensateonanAtomChip -- 4.Summary -- References -- Chapter10BOSE-FERMIMIXTURESOFULTRACOLDATOMS -- Abstract -- 1.Introduction -- 2.GroundState -- 2.1.Mean-FieldandThomas-FermiApproximations -- 2.2.QualitativeStudyofGroundState -- 2.3.NumericalResults -- 3.CollectiveOscillation -- 3.1.SumRules -- 3.2.CollectiveOscillationsinBose-FermiMixtures -- 4.Instability -- 5.MolecularFormationsinBose-fermiMixtures -- 6.Summary -- References -- INDEX.

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