An Advanced Course in Computational Nuclear Physics: Bridging the Scales from Quarks to Neutron Stars PDF
Preview An Advanced Course in Computational Nuclear Physics: Bridging the Scales from Quarks to Neutron Stars
Lecture Notes in Physics 936 Morten Hjorth-Jensen Maria Paola Lombardo Ubirajara van Kolck Editors An Advanced Course in Computational Nuclear Physics Bridging the Scales from Quarks to Neutron Stars Lecture Notes in Physics Volume 936 FoundingEditors W.Beiglböck J.Ehlers K.Hepp H.Weidenmüller EditorialBoard M.Bartelmann,Heidelberg,Germany P.HaRnggi,Augsburg,Germany M.Hjorth-Jensen,Oslo,Norway R.A.L.Jones,Sheffield,UK M.Lewenstein,Barcelona,Spain H.vonLöhneysen,Karlsruhe,Germany A.Rubio,Hamburg,Germany M.Salmhofer,Heidelberg,Germany W.Schleich,Ulm,Germany S.Theisen,Potsdam,Germany D.Vollhardt,Augsburg,Germany J.Wells,AnnArbor,USA G.P.Zank,Huntsville,USA The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new devel- opmentsin physicsresearch and teaching-quicklyand informally,but with a high qualityand the explicitaim to summarizeand communicatecurrentknowledgein anaccessibleway.Bookspublishedinthisseriesareconceivedasbridgingmaterial between advanced graduate textbooks and the forefront of research and to serve threepurposes: (cid:129) to be a compact and modern up-to-date source of reference on a well-defined topic (cid:129) to serve as an accessible introduction to the field to postgraduate students and nonspecialistresearchersfromrelatedareas (cid:129) to be a source of advanced teaching material for specialized seminars, courses andschools Bothmonographsandmulti-authorvolumeswillbeconsideredforpublication. 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Proposalsshouldbe sent to a memberof the EditorialBoard, ordirectly to the managingeditoratSpringer: ChristianCaron SpringerHeidelberg PhysicsEditorialDepartmentI Tiergartenstrasse17 69121Heidelberg/Germany [email protected] Moreinformationaboutthisseriesathttp://www.springer.com/series/5304 Morten Hjorth-Jensen (cid:129) Maria Paola Lombardo (cid:129) Ubirajara van Kolck Editors An Advanced Course in Computational Nuclear Physics Bridging the Scales from Quarks to Neutron Stars 123 Editors MortenHjorth-Jensen MariaPaolaLombardo NationalSuperconductingCyclotron INFN,LaboratoriNazionalidiFrascati LaboratoryandDepartmentofPhysics FrascatiRoma,Italy andAstronomy MichiganStateUniversity EastLansing,Michigan USA DepartmentofPhysics UniversityofOslo Oslo,Norway UbirajaravanKolck DepartmentofPhysics UniversityofArizona Tucson,AZ USA ISSN0075-8450 ISSN1616-6361 (electronic) LectureNotesinPhysics ISBN978-3-319-53335-3 ISBN978-3-319-53336-0 (eBook) DOI10.1007/978-3-319-53336-0 LibraryofCongressControlNumber:2017937055 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Thisgraduate-leveltextcollectsandsynthesizestenseriesoflecturesonthenuclear quantum many-body problem—starting from our present understanding of the underlyingforceswith a presentationof recentadvanceswithin thefield of lattice quantumchromodynamicsviaeffectivefieldtheoriestocentralmany-bodymethods like Monte Carlo methods, coupled cluster theories, the similarity renormaliza- tion group approach, Green’s function methods, and large-scale diagonalization approaches. In particular algorithmic and computationaladvances show promise for break- throughs in predictive power including proper error estimates and a better under- standingoftheunderlyingeffectivedegreesoffreedomandoftherespectiveforces atplay. Enabled by recent advances in theoretical, experimental, and numerical tech- niques,themodernandstate-of-theartapplicationsconsideredinthisvolumespan theentirerangefromoursmallestcomponents,quarksandgluons,asthemediators ofthestrongforcetothecomputationoftheequationofstateforneutronstarmatter. The present lectures provide a proper exposition of the underlying theoretical andalgorithmicapproachesaswellasstrongtiestothenumericalimplementation of the exposed methods. Several of the lectures provide links to actual numerical software and benchmark calculations, allowing eventual readers, based upon the availablematerial,to developtheirownprogramsfortacklingchallengingnuclear many-bodyproblems. EastLansing,MI,USAandOslo,Norway MortenHjorth-Jensen FrascatiRoma,Italy MariaPaolaLombardo Tucson,AZ,USAandParis,France UbirajaravanKolck v Contents 1 MotivationandOverarchingAims ....................................... 1 MortenHjorth-Jensen,MariaPaolaLombardo, andUbirajaravanKolck 2 QuantumChromodynamics............................................... 5 ThomasSchäfer 2.1 Introduction........................................................... 5 2.2 PathIntegralsandtheMetropolisAlgorithm ....................... 6 2.3 QuantumChromodynamics.......................................... 11 2.3.1 QCDatZeroTemperatureandDensity.................... 11 2.3.2 QCDatFiniteTemperature ................................ 15 2.3.3 HighBaryonDensityQCD ................................ 17 2.4 LatticeQCD.......................................................... 18 2.4.1 TheWilsonAction.......................................... 18 2.4.2 FermionsontheLattice .................................... 21 2.4.3 TheQCDVacuum.......................................... 23 2.4.4 LatticeQCDatFiniteBaryonDensity .................... 27 2.4.5 RealTimeProperties....................................... 29 2.5 NonequilibriumQCD................................................ 31 2.5.1 FluidDynamics............................................. 32 2.5.2 ComputationalFluidDynamics............................ 34 2.5.3 KineticTheory.............................................. 37 2.5.4 ClassicalFieldTheory...................................... 40 2.5.5 NonequilibriumQCD:Holography........................ 42 2.6 OutlookandAcknowledgments..................................... 48 Appendix:Z2GaugeTheory ................................................ 49 References.................................................................... 51 vii viii Contents 3 LatticeQuantumChromodynamics...................................... 55 TetsuoHatsuda 3.1 Introduction........................................................... 55 3.1.1 EuclideanQCDAction..................................... 56 3.1.2 QuantumFluctuations...................................... 57 3.2 LatticeQCD:TheoreticalBasis ..................................... 57 3.2.1 WilsonLine................................................. 57 3.2.2 LatticeGluons .............................................. 59 3.2.3 LatticeFermions............................................ 60 3.2.4 PartitionFunctionontheLattice........................... 63 3.2.5 StrongCouplingExpansionandQuarkConfinement..... 65 3.2.6 WeakCouplingExpansionandContinuumLimit ........ 68 3.2.7 RunningCoupling.......................................... 70 3.3 LatticeQCD:NumericalSimulations............................... 72 3.3.1 ImportanceSampling....................................... 72 3.3.2 MarkovChainMonteCarlo(MCMC)..................... 72 3.3.3 HybridMonteCarlo(HMC) ............................... 74 3.3.4 ErrorEstimate .............................................. 76 3.3.5 HeavyQuarkPotential ..................................... 77 3.3.6 MassesofLightHadrons................................... 78 3.4 LatticeQCDandNuclearForce..................................... 80 3.4.1 MasterEquationforBaryon-BaryonInteraction.......... 81 3.4.2 Baryon-BaryonInteractioninFlavorSU(3)Limit........ 82 3.5 Exercises.............................................................. 85 Appendix..................................................................... 86 References.................................................................... 91 4 GeneralAspectsofEffectiveFieldTheoriesandFew-Body Applications................................................................. 93 Hans-WernerHammerandSebastianKönig 4.1 Introduction:DimensionalAnalysisandtheSeparation ofScales .............................................................. 93 4.2 TheoreticalFoundationsofEffectiveFieldTheory................. 95 4.2.1 Top-Downvs.Bottom-UpApproaches.................... 96 4.2.2 NonrelativisticFieldTheory ............................... 100 4.2.3 SymmetriesandPowerCounting.......................... 110 4.2.4 Matching.................................................... 117 4.3 EffectiveFieldTheoryforStronglyInteractingBosons............ 117 4.3.1 EFTforShort-RangeInteractions ......................... 118 4.3.2 DimerFieldFormalism..................................... 123 4.3.3 Three-BodySystem ........................................ 124 4.3.4 Three-BodyObservables................................... 127 4.3.5 RenormalizationGroupLimitCycle ...................... 130 Contents ix 4.4 EffectiveFieldTheoryforNuclearFew-BodySystems............ 133 4.4.1 Overview.................................................... 133 4.4.2 PionlessEffectiveFieldTheory............................ 133 4.4.3 TheTwo-NucleonS-WaveSystem ........................ 134 4.4.4 ThreeNucleons:ScatteringandBoundStates ............ 138 4.5 BeyondShort-RangeInteractions:AddingPhotonsandPions .... 143 4.5.1 ElectromagneticInteractions............................... 143 4.5.2 Example:DeuteronBreakup............................... 148 4.5.3 ChiralEffectiveFieldTheory.............................. 150 References.................................................................... 152 5 LatticeMethodsandEffectiveFieldTheory ............................ 155 AmyNicholson 5.1 Introduction........................................................... 155 5.2 BasicsofEffectiveFieldTheoryandLatticeEffectiveField Theory ................................................................ 157 5.2.1 PionlessEffectiveFieldTheory............................ 157 5.2.2 LatticeEffectiveFieldTheory ............................. 163 5.3 CalculatingObservables ............................................. 176 5.3.1 Signal-to-Noise............................................. 178 5.3.2 StatisticalOverlap.......................................... 185 5.3.3 InterpolatingFields......................................... 190 5.3.4 AnalysisMethods........................................... 195 5.4 SystematicErrorsandImprovement ................................ 200 5.4.1 ImprovingtheKineticEnergyOperator................... 200 5.4.2 ImprovingtheInteraction .................................. 203 5.4.3 ScalingofDiscretizationErrorsforMany-Body Systems ..................................................... 211 5.4.4 AdditionalSourcesofSystematicError................... 214 5.5 BeyondLeadingOrderEFT ......................................... 216 5.5.1 TuningtheEffectiveRange ................................ 217 5.5.2 IncludingPions............................................. 222 5.5.3 3-andHigher-BodyInteractions........................... 224 5.5.4 FinalConsiderations........................................ 228 5.6 ReadingAssignmentsandExercises................................ 229 Appendix..................................................................... 230 References.................................................................... 231 6 LatticeMethodsandtheNuclearFew-andMany-BodyProblem.... 237 DeanLee 6.1 Introduction........................................................... 237 6.2 RecentApplications.................................................. 238 6.3 ScatteringontheLattice ............................................. 239 6.4 LatticeFormalisms................................................... 241 6.4.1 GrassmannPathIntegral ................................... 242 6.4.2 TransferMatrixOperator................................... 244 x Contents 6.4.3 GrassmannPathIntegralwithAuxiliaryField............ 246 6.4.4 TransferMatrixOperatorwithAuxiliaryField ........... 248 6.5 ProjectionMonteCarlo .............................................. 249 6.6 ImportanceSampling ................................................ 253 6.7 Exercises.............................................................. 257 6.8 CodesandBenchmarks.............................................. 258 References.................................................................... 260 7 AbInitioMethodsforNuclearStructureandReactions:From FewtoManyNucleons..................................................... 263 GiuseppinaOrlandini 7.1 Introduction:Theory,Model,Method............................... 263 7.2 TheNon-relativisticQuantumMechanicalMany-Nucleon Problem............................................................... 264 7.2.1 TranslationandGalileianInvariance ...................... 265 7.3 ClassificationofAbInitioApproachesforGround-State Calculations .......................................................... 266 7.3.1 TheFaddeev-Yakubowski(FY)Method .................. 266 7.3.2 MethodsBased on the VariationalTheorem (DiagonalizationMethods)................................. 267 7.3.3 MethodsBasedonSimilarityTransformations ........... 270 7.3.4 MonteCarloMethods...................................... 273 7.4 TwoDiagonalizationMethodswithEffectiveInteractions......... 274 7.4.1 TheNoCoreShellModelMethod(NCSM) .............. 274 7.4.2 The Hyperspherical Harmonics Method withEffectiveInteraction(EIHH) ......................... 275 7.5 ExcitedStates......................................................... 276 7.5.1 ResponseFunctionstoPerturbativeProbes............... 277 7.6 IntegralTransformApproaches...................................... 281 7.6.1 SumRules................................................... 281 7.6.2 IntegralTransformwiththeLaplaceKernel .............. 282 7.6.3 IntegralTransformwiththeLorentzianKernel ........... 283 7.6.4 IntegralTransformwiththeSumuduKernel.............. 285 7.6.5 IntegralTransformwiththeStieltjesKernel .............. 287 7.6.6 MethodsofInversion....................................... 288 7.7 Conclusion............................................................ 290 References.................................................................... 290 8 ComputationalNuclearPhysicsandPostHartree-FockMethods.... 293 JustinG.Lietz,SamuelNovario,GustavR.Jansen,GauteHagen, andMortenHjorth-Jensen 8.1 Introduction........................................................... 293 8.2 Single-Particle Basis, Hamiltonians and Models fortheNuclearForce................................................. 295 8.2.1 IntroductiontoNuclearMatterandHamiltonians ........ 295 8.2.2 Single-ParticleBasisforInfiniteMatter................... 302
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