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[美] 博赫姆 著 / 科学出版社 / 2009-03 / 精装
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国外物理名著系列26:量子系统中的几何相位基本原理、数学概念及其在分子物理和凝聚态物理中的应用
Aimedatgraduatephysicsandchemistrystudents,thisisthefirstcomprechenslvemonographcoveringtheconceptofthe
geometricphaseinquantumphysicsfromitsmathematicalfoundationstoitsphysicalapplicationsandexperimentalmanifestations.ItcontainsallthepremisesoftheadiabaticBerryphaseaswellastheexactAnandan-Aharonovphase.Itdiscussesquantumsystemsinaclassicaltime-independentenvironment(timedependentHamiltonians)andquantumsystemsinachangingenvironment(gaugetheoryofmolecularphysics).ThemathematicalmethodsusedareacombinationofdifferentialgeometryandthetheoryofIinearoperatorsinHilbertSpace.Asaresult,themonographdemonstrateshownon-trivialgaugetheoriesnaturallyariseandhowtheconsequencescanbeexperimentallyobserved.Readersbenefitbygainingadeepunderstandingofthelong-ignoredgaugetheoreticeffectsofquantummethanicsandhowtomeasurethem.
1Introduction2QuantalPhaseFactorsforAdiabaticChanges2.1Introduction2.2AdiabaticApproximation2.3BerrysAdiabaticPhase2.4TopologicalPhasesandtheAharonov-BohmEffectProblems3SpinningQuantumSysteminanExternalMagneticField3.1Introduction3.2TheParameterizationoftheBasisVectors3.3Mead-BerryConnectionandBerryPhaseforAdiabaticEvolutions-MagneticMonopolePotentials3.4TheExactSolutionoftheSchrSdingerEquation3.5DynamicalandGeometricalPhaseFactorsforNon-AdiabaticEvolutionProblems4QuantalPhasesforGeneralCyclicEvolution4.1Introduction4.2Aharonov-AnandanPhase4.3ExactCyclicEvolutionforPeriodicHamiltoniansProblems5FiberBundlesandGaugeTheories5.1Introduction5.2FromQuantalPhasestoFiberBundles5.3AnElementaryIntroductiontoFiberBundles5.4GeometryofPrincipalBundlesandtheConceptofHolonomy5.5GaugeTheories5.6MathematicalFoundationsofGaugeTheoriesandGeometryofVectorBundlesProblems6MathematicalStructureoftheGeometricPhaseI:TheAbelianPhase6.1Introduction6.2HolonomyInterpretationsoftheGeometricPhase6.3ClassificationofU(1)PrincipalBundlesandtheRelationBetweentheBerry-SimonandAharonov-AnandanInterpretationsoftheAdiabaticPhase6.4HolonomyInterpretationoftheNon-AdiabaticPhaseUsingaBundleovertheParameterSpace6.5SpinningQuantumSystemandTopologicalAspectsoftheGeometricPhaseProblems7MathematicalStructureoftheGeometricPhaseII:TheNon-AbelianPhase7.1Introduction7.2TheNon-AbelianAdiabaticPhase7.3TheNon-AbelianGeometricPhase7.4HolonomyInterpretationsoftheNon-AbelianPhase7.5ClassificationofU(N)PrincipalBundlesandtheRelationBetweentheBerry-SimonandAharonov-AnandanInterpretationsofNon-AbelianPhaseProblems8AQuantumPhysicalSysteminaQuantumEnvironment-TheGaugeTheoryofMolecularPhysics8.1Introduction8.2TheHamiltonianofMolecularSystems8.3TheBorn-OppenheimerMethod8.4TheGaugeTheoryofMolecularPhysics8.5TheElectronicStatesofDiatomicMolecule8.6TheMonopoleoftheDiatomicMoleculeProblems9CrossingofPotentialEnergySurfacesandtheMolecularAharonov-BohmEffect9.1Introduction9.2CrossingofPotentialEnergySurfaces9.3ConicalIntersectionsandSign-ChangeofWaveFunctions9.4ConicalIntersectionsinJahn-TellerSystems9.5SymmetryOftheGroundStateinJahn-TellerSystems9.6GeometricPhaseinTwoKramersDoubletSystems9.7Adiabatic-DiabaticTransformation10.ExperimentalDetectionofGeometricPhasesIQuantumSystemsinClassicalEnvironments10.1Introduction10.2TheSpinBerryPhaseControlledbyMagneticFields10.2.1SpinsinMagneticFields:TheLaboratoryFrame10.2.2SpinsinMagneticFields:TheRotatingFrame10.2.3AdiabaticReorientationinZeroField10.3ObservationoftheAharonov-AnandanPhaseThroughtheCyclicEvolutionofQuantumStatesProblems11.ExperimentalDetectionofGeometricPhasesII:QuantumSystemsinQuantumEnvironments11.1Introduction11.2InternalRotorsCoupledtoExternalRotors11,3Electronic-RotationalCoupling11.4VibronicProblemsinJahn-TellerSystems11.4.1TransitionMetalIonsinCrystals11.4.2HydrocarbonRadicals11.4.3AlkaliMetalTrimers11.5TheGeometricPhaseinChemicalReactions12.GeometricPhaseinCondensedMatterI:BlochBands12.1Introduction12.2BlochTheory12.2.1One-DimensionalCase12.2.2Three-DimensionalCase12.2.3BandStructureCalculation12.3SemiclassicalDynamics12.3.1EquationsofMotion12.3.2SymmetryAnalysis12.3.3DerivationoftheSemiclassicalFormulas12.3.4Time-DependentBands12.4ApplicationsofSemiclassicalDynamics12.4.1UniformDCElectricField12.4.2UniformandConstantMagneticField12.4.3Per12.5.1GeneralProperties12.5.2LocalizationProperties12.6SomeIssuesonBandInsulators12.6.1QuantizedAdiabaticParticleTransport12.6.2PolarizationProblems13.GeometricPhaseinCondensedMatterII:TheQuantumHallEffect13.1Introduction13.2BasicsoftheQuantumHallEffect13.2.1TheHaltEffect13.2.2TheQuantumHallEffect13.2.3TheIdealModel13.2.4CorrectionstoQuantization13.3MagneticBandsinPeriodicPotentials13.3.1Single-BandApproximationinaWeakMagneticField13.3.2HarpersEquationandHofstadtersButterfly13.3.3MagneticTranslations13.3.4QuantizedHallConductivity13.3.5EvaluationoftheChernNumber13.3.6SemiclassicalDynamicsandQuantization13.3.7StructureofMagneticBandsandHyperorbitLevels13.3.8HierarchicalStructureoftheButterfly13.3.9QuantizationofHyperorbitsandRuleofBandSplitting13.4QuantizationofHallConductanceinDisorderedSystems13.4.1SpectrumandWaveFunctions13.4.2PerturbationandScatteringTheory13.4.3LaughlinsGaugeArgument13.4.4HallConductanceasaTopologicalInvariant14.GeometricPhaseinCondensedMatterIII:Many-BodySystems14.1Introduction14.2FractionalQuantumHallSystems14.2.1LaughlinWaveFunction14.2.2FractionalChargedExcitations14.2.3FractionalStatistics14.2.4DegeneracyandFractionalQuantization14.3Spin-WaveDynamicsinItinerantMagnets14.3.1GeneralFormulation14.3.2Tight-BindingLimitandBeyond14.3.3SpinWaveSpectrum14.4GeometricPhaseinDoubly-DegenerateElectronicBandsProblemA.AnElementaryIntroductiontoManifoldsandLieGroupsA.1IntroductionA.2DifferentiableManifoldsA.3LieGroupsB.ABriefReviewofPointGroupsofMoleculeswithA
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