in strongly correlated electron physics a dmft 在强关联电子物理的龋齿问题课件

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1、Quasi-exactlysolvablemodelsinquantummechanicsandLiealgebrasS.N.DolyaB.VerkinInstituteforLowTemperaturePhysicsandEngineeringoftheNationalAcademyofSciencesofUkraineS.N.DolyaJMP,50(2009)S.N.DolyaJMP,49(2008).S.N.DolyaO.B.ZaslavskiiJ.Phys.A:Math.Gen.34(2001)S.N.DolyaO.B.ZaslavskiiJ.Phys.A

2、:Math.Gen.34(2001)S.N.DolyaO.B.ZaslavskiiJ.Phys.A:Math.Gen.33(2000)Outline1.QES-extension(A)2.quadraticQES-Liealgebras3.physicalapplications4.QES-extension(B)5.cubicQES-Liealgebrassl2(R)-HamiltoniansRepresentation:InvariantsubspaceTurbineretal(partialalgebraization)Whatisbeingstudied?

3、HamiltoniansareformulatedintermsofQESLiealgebras.eigenvaluesandeigenfunctionswhenpossible.Invariantsubspaces:Howthisisbeingstudied?NonlinearQESLiealgebrasQES-extension:0.ourstrategyWefindageneralformoftheoperatorofthesecondorderP2forwhichsubspaceM2=span{f1,f2}ispreserved.Wemakeextensi

4、onofthesubspaceM2→M4=span{f1,f2,f3,f4}WefindageneralformoftheoperatorofthesecondorderP4forwhichsubspaceM4ispreserved.weobtaintheexplicitformofoperatorP2(N+1)thatactsontheelementsofthesubspaceM2(N+1)={f1,f2,…,f2(N+1)}QES-extension:;I.SelecttheminimalinvariantsubspaceSelecttheinvarianto

5、peratorConditionforthesubspaceM2QES-extension:II.extensionfortheminimalinvariantsubspaceConditionforthesubspaceM4QES-extension:ConditionsoftheQES-extension:12WronskianmatrixIII.ExtensionfortheminimalinvariantsubspaceOrderofderivativeshypergeometricfunctionRealization(specialfunctions:

6、hypergeometric,Airy,Besselones)QES-extension:ParticularchoiceofQESextensionactmoreQES-extension:Example1counterQES-extension:ThecommutationrelationsoftheoperatorsCasimiroperator:CasimirinvariantQES-extension:Example2counterQES-extension:ThecommutationrelationsoftheoperatorsCasimirinva

7、riantCasimiroperator:QES-extension:Example3counterQES-extension:ThecommutationrelationsoftheoperatorsTwo-photonRabiHamiltonianRabiHamiltoniandescribesatwo-levelsystem(atom)coupledtoasinglemodeofradiationviadipoleinteraction.Two-photonRabiHamiltonianThetwo-photonRabiHamiltonianThetwo-p

8、hoton