Normalization and global analysis of perturbations of the hydrogen atom

Normalization and global analysis of perturbations of the hydrogen atom

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時間:2019-06-27

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1、REVIEWSOFMODERNPHYSICS,VOLUME82,JULY–SEPTEMBER2010NormalizationandglobalanalysisofperturbationsofthehydrogenatomK.Efstathiou*DepartmentofMathematics,UniversityofGroningen,Groningen9700AK,TheNetherlands?D.A.SadovskiíDépartementdePhysique,UniversitéduLi

2、ttoral–C?ted’Opale,59140Dunkerque,FrancePublished3August2010ThehydrogenatomperturbedbysufTcientlysmallhomogeneousstaticelectricandmagneticTeldsofarbitrarymutualalignmentisaspeciTcperturbationoftheKeplersystemwiththreedegreesoffreedomandthreeparamete

3、rs.NormalizationoftheKepleriansymmetryrevealsthattheparameterspaceisstratiTedintoresonantzonesofsystems,eachzonewithaninternaldynamicalstratiTcationofitsownEfstathiou,Sadovski,andZhilinski,2007,Proc.R.Soc.London,Ser.A463,1771.Basedonthefullyintegrab

4、leapproximation,thebundleofinvarianttoriofindividualsystemswithinzonesischaracterizedgloballyandthequalitativedynamicalstratiTcationisuncovered.Thetechniquesinvolvedinthisanalysisareillustratedwiththeexampleofthe1:1resonancezonenearorthogonalTeldswh

5、osestructureisknownatpresent.Applicationsinthecorrespondingquantumsystemarealsodescribed.DOI:10.1103/RevModPhys.82.2099PACSnumbers:32.60.i,03.65.Vf,45.05.x,03.65.SqCONTENTS4.Generalizedorfractionalmonodromy21105.Monodromymapanditsmatrix2111E.Quant

6、um-classicalcorrespondence2111I.Introduction21001.Quantumjointspectrumlattice2111A.Globaldynamicalanalysis21002.Quantummonodromy21121.Characteristicsofindividualperturbations21003.Generalizations21122.StratiTcationoftheparameterspace2101F.Mainconjectu

7、reoftheglobalclassiTcation2112B.Hamiltonianandparameterspace21011.ToricTbrationsandtheirBD2112C.Historicaloverviewandperspective21022.RecoveringtopologyofsingularTbrationsD.Structureofthepaper2102fromtheirBD2113II.BasicMathematicalConcepts21033.Extend

8、ingtosystemswithhyperbolicA.Regularization,Trstintegrals,andtheir?ows2103singularTbers2113B.Geometryofthereductionmap21034.Extendingtonearlyintegrablesystems21131.FirstorKeplerianreduction2103III.Results:QualitativeTypesofPerturbations21132.Re

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