BERRY PHASE PHYSICS IN FREE AND INTERACTING FERMIONIC SYSTEMS自由和相互作用费米子系统中地BRIME相位物理学.pdf

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1、THEUNIVERSITYOFCHICAGOBERRYPHASEPHYSICSINFREEANDINTERACTINGFERMIONICSYSTEMSADISSERTATIONSUBMITTEDTOTHEFACULTYOFTHEDIVISIONOFTHEPHYSICALSCIENCESINCANDIDACYFORTHEDEGREEOFDOCTOROFPHILOSOPHYDEPARTMENTOFPHYSICSBYJINGYUANCHENCHICAGO,ILLINOISJUNE2016arXiv:1608.03568

2、v2[cond-mat.mes-hall]8Jun2017TABLEOFCONTENTSLISTOFFIGURES....................................ivLISTOFTABLES.....................................vACKNOWLEDGMENTS.................................viABSTRACT........................................viii1INTRODUCTIO

3、N...................................11.1Background,ProblemsandResults.......................11.2OrganizationoftheThesis............................91.3ConventionsintheThesis............................112BERRYFERMIGAS.................................132.1Revi

4、ewofSymplecticFormulationofClassicalMechanics...........132.1.1WorldlineParametrizedbyTime....................132.1.2WorldlineParametrizedbyIntrinsicParameter.............182.2Semi-ClassicalParticlewithBerryPhase....................202.3EnsembleofBerryFermiGa

5、s..........................232.3.1BoltzmannEquationandCurrent....................232.3.2AnomalousHallEect..........................272.3.3EquilibriumCurrent...........................282.4DerivationfromPathIntegral..........................292.5Example:Chira

6、lKineticTheoryofWeylFermion...............372.5.1SingleWeylFermion...........................382.5.2Ensemble.................................422.5.3ChiralMagneticEect..........................442.6ChiralAnomalyinChiralKineticTheory....................472.7Su

7、mmaryandOutlook..............................513LORENTZSYMMETRYINCHIRALKINETICTHEORY............533.1Puzzle.......................................533.2Non-TrivialFrameDependence.........................553.2.1InnitesimalTransformation.......................5

8、73.2.2FiniteTransformationOn-Shell.....................593.2.3Current,Stress-EnergyTensorandPhysicalInterpretation......593.3RelationtoWignerTranslation.........................623.4Chira