中外物理学精品书系：玻色-爱因斯坦凝聚的基础与前沿（英文影印版）

图书标准信息

• 作者 [日]上田正仁 著
• 出版社 北京大学出版社
• 出版时间 2015-01
• 版次 1
• ISBN 9787301251737
• 定价 63.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 372页
• 字数 371千字
• 正文语种 简体中文，英语
• 原版书名 Fundamentals and New Frontiers of Bose-Einstein Condensation
• 丛书 中外物理学精品书系

【内容简介】

　　《中外物理学精品书系：玻色-爱因斯坦凝聚的基础与前沿（英文影印版）》首先介绍了玻色-爱因斯坦凝聚（BEC）的基本理论。之后，《中外物理学精品书系：玻色-爱因斯坦凝聚的基础与前沿（英文影印版）》讨论了快速旋转BEC，旋量和偶极BEC，低维BEC等近来发展迅速的方向。本书还介绍了平衡或非平衡费米液体超流，包括BCS-BEC交叉、幺正气体、p波超流等。本书适合本领域的研究者和研究生阅读。

【作者简介】

　　（日）上田正仁，日本东京大学教授。

【目录】

Prefacev
1.FundamentalsofBose-EinsteinCondensation1
1.1IndistinguishabilityofIdenticalParticles..........1
1.2IdealBoseGasinaUniformSystem............3
1.3Off-DiagonalLong-RangeOrder:BoseSystem......6
1.4Off-DiagonalLong-RangeOrder:FermiSystem......10
1.5U(1)GaugeSymmetry....................11
1.6Ground-StateWaveFunctionofaBoseSystem......13
1.7BECandSuperfluidity....................15
1.8Two-FluidModel.......................20
1.9FragmentedCondensate...................23
1.9.1Two-statemodel...................23
1.9.2Degeneratedouble-wellmodel...........25
1.9.3Spin-1antiferromagneticBEC...........27
1.10InterferenceBetweenIndependentCondensates......28
1.11FeshbachResonance.....................31
2.WeaklyInteractingBoseGas33
2.1InteractionsBetweenNeutralAtoms............33
2.2Pseudo-PotentialMethod..................36
2.3BogoliubovTheory......................40
2.3.1Bogoliubovtransformations.............40
2.3.2Bogoliubovgroundstate..............45
2.3.3Low-lyingexcitationsandcondensatefraction..48
2.3.4PropertiesofBogoliubovgroundstate.......50
2.4BogoliubovTheoryofQuasi-One-DimensionalTorus...54
2.4.1CaseofBECatrest:stabilityofBEC.......55
2.4.2CaseofrotatingBEC:Landaucriterion......56
2.4.3GroundstateofBECinrotatingtorus......59
2.5Bogoliubov-deGennes(BdG)Theory...........60
2.6MethodofBinaryCollisionExpansion...........65
2.6.1Equationofstate..................65
2.6.2Clusterexpansionofpartitionfunction......66
2.6.3IdealBoseandFermigases.............67
2.6.4Matsubaraformula.................69
3.TrappedSystems73
3.1IdealBoseGasinaHarmonicPotential..........73
3.1.1Transitiontemperature...............75
3.1.2Condensatefraction.................76
3.1.3Chemicalpotential.................77
3.1.4Specificheat.....................77
3.2BECinOne-andTwo-DimensionalParabolicPotentials.79
3.2.1Densityofstates...................79
3.2.2Transitiontemperature...............79
3.2.3Condensatefraction.................80
3.3SemiclassicalDistributionFunction.............81
3.4Gross-PitaevskiiEquation..................83
3.5Thomas-FermiApproximation...............84
3.6CollectiveModesintheThomas-FermiRegime......88
3.6.1Isotropicharmonicpotential............89
3.6.2Axisymmetrictrap.................91
3.6.3Scissorsmode....................92
3.7VariationalMethod......................93
3.7.1Gaussianvariationalwavefunction........94
3.7.2Collectivemodes...................96
3.8AttractiveBose-EinsteinCondensate............98
3.8.1Collectivemodes...................99
3.8.2Collapsingdynamicsofanattractivecondensate.102
4.LinearResponseandSumRules105
4.1LinearResponseTheory...................105
4.1.1Linearresponseofdensityfluctuations......105
4.1.2Retardedresponsefunction.............108
4.2SumRules...........................109
4.2.1Longitudinalf-sumrule..............110
4.2.2Compressibilitysumrule..............112
4.2.3Zeroenergygaptheorem..............114
4.2.4Josephsonsumrule.................115
4.3Sum-RuleApproachtoCollectiveModes..........120
4.3.1Excitationoperators.................121
4.3.2Virialtheorem....................122
4.3.3Kohntheorem....................123
4.3.4Isotropictrap....................124
4.3.5Axisymmetrictrap.................127
5.StatisticalMechanicsofSuperfluidSystemsinaMovingFrame129
5.1TransformationtoMovingFrames.............129
5.2ElementaryExcitationsofaSuperfluid...........131
5.3LandauCriterion.......................133
5.4CorrelationFunctionsatThermalEquilibrium......134
5.5NormalFluidDensity....................136
5.6Low-LyingExcitationsofaSuperfluid...........140
5.7Examples...........................141
5.7.1IdealBosegas....................141
5.7.2WeaklyinteractingBosegas............143
6.SpinorBose-EinsteinCondensate145
6.1InternalDegreesofFreedom.................145
6.2GeneralHamiltonianofSpinorCondensates........146
6.3Spin-1BEC..........................151
6.3.1Mean-fieldtheoryofaspin-1BEC.........153
6.3.2Many-bodystatesinsingle-modeapproximation.157
6.3.3Superflow,spintexture,andBerryphase.....161
6.4Spin-2BEC..........................163
7.Vortices171
7.1HydrodynamicTheoryofVortices.............171
7.2QuantizedVortices......................174
7.3InteractionBetweenVortices................180
7.4VortexLattice........................181
7.4.1Dynamicsofvortexnucleation...........181
7.4.2Collectivemodesofavortexlattice........183
7.5FractionalVortices......................186
7.6SpinCurrent.........................187
7.7FastRotatingBECs.....................189
7.7.1LowestLandaulevelapproximation........189
7.7.2MeanfieldquantumHallregime..........192
7.7.3Many-bodywavefunctionsofafast
rotatingBEC....................194
8.FermionicSuperfluidity197
8.1IdealFermiGas........................197
8.2FermiLiquidTheory.....................200
8.3CooperProblem.......................205
8.3.1Two-bodyproblem.................205
8.3.2Many-bodyproblem.................209
8.4Bardeen-Cooper-Schrieffer(BCS)Theory.........211
8.5BCS-BECCrossoveratT=0................215
8.6SuperfluidTransitionTemperature.............219
8.7BCS-BECCrossoveratT_=0................221
8.8Gor'kov-Melik-BarkhudarovCorrection..........225
8.9UnitaryGas..........................228
8.10ImbalancedFermiSystems..................231
8.11P-WaveSuperfluid......................234
8.11.1Generalizedpairingtheory.............234
8.11.2Spin-tripletp-wavestates..............238
9.Low-DimensionalSystems241
9.1Non-interactingSystems...................241
9.2Hohenberg-Mermin-WagnerTheorem...........243
9.3Two-DimensionalBECatAbsoluteZero..........246
9.4Berezinskii-Kosterlitz-ThoulessTransition.........247
9.4.1Universaljump....................247
9.4.2Quasilong-rangeorder...............249
9.4.3Renormalization-groupanalysis..........250
9.5QuasiOne-DimensionalBEC................252
9.6Tonks-GirardeauGas....................256
9.7Lieb-LinigerModel......................258
10.DipolarGases261
10.1Dipole-DipoleInteraction..................261
10.1.1Basicproperties...................261
10.1.2Orderofmagnitudeandlengthscale.......263
10.1.3D-wavenature....................264
10.1.4Tuningthedipole-dipoleinteraction........265
10.2PolarizedDipolarBEC....................266
10.2.1NonlocalGross-Pitaevskiiequation........266
10.2.2Stability.......................267
10.2.3Thomas-Fermilimit.................269
10.2.4Quasitwo-dimensionalsystems...........271
10.3Spinor-DipolarBEC.....................273
10.3.1Einstein-deHaaseffect...............274
10.3.2Fluxclosureandground-statecirculation.....274
11.OpticalLattices277
11.1OpticalPotential.......................277
11.1.1Opticaltrap.....................277
11.1.2Opticallattice....................280
11.2BandStructure........................283
11.2.1Blochtheorem....................283
11.2.2Brillouinzone....................285
11.2.3Blochoscillations..................286
11.2.4Wannierfunction..................287
11.3Bose-HubbardModel....................288
11.3.1Bose-HubbardHamiltonian............288
11.3.2Superfluid-Mott-insulatortransition........289
11.3.3Phasediagram....................291
11.3.4Mean-fieldapproximation..............292
11.3.5Supersolid......................295
12.TopologicalExcitations297
12.1HomotopyTheory......................297
12.1.1Homotopicrelation.................297
12.1.2Fundamentalgroup.................299
12.1.3Higherhomotopygroups..............302
12.2OrderParameterManifold..................303
12.2.1Isotropygroup....................303
12.2.2Spin-1BEC.....................304
12.2.3Spin-2BEC.....................305
12.3ClassificationofDefects...................306
12.3.1Domains.......................306
12.3.2Linedefects.....................306
12.3.3Pointdefects.....................311
12.3.4Skyrmions......................313
12.3.5Influenceofdifferenttypesofdefects.......316
12.3.6Topologicalcharges.................318
AppendixAOrderofPhaseTransition,Clausius-Clapeyron
Formula,andGibbs-DuhemRelation321
AppendixBBogoliubovWaveFunctionsinCoordinateSpace323
B.1Ground-StateWaveFunction...........323
B.2One-PhononState.................327
AppendixCEffectiveMass,SoundVelocity,andSpin
SusceptibilityofFermiLiquid329
AppendixDDerivationofEq.(8.155)333
AppendixEf-SumRule335
Bibliography337
Index347