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一维和二维关联无序安德森模型演示文稿当前1页,总共24页。一维和二维关联无序安德森模型当前2页,总共24页。
One-andtwo-dimensionalAndersonmodelwithlong-rangecorrelated-disorderAndersonmodel-IntroductionEntanglementin1D2DEntanglement2Dconductance2Dtransmission2Dmagnetoconductance当前3页,总共24页。Andersonmodel-IntroductionWhatisadisorderedsystem?Nolong-rangetranslationalorderTypesofdisorder
(a)crystal(b)Componentdisorder(c)positiondisorder(d)topologicaldisorder当前4页,总共24页。diagonaldisorder
off-diagonaldisordercompletedisorderLocalizationprediction:anelectron,whenplacedinastrongdisorderedlattice,willbeimmobile[1]P.W.Anderson,Phys.Rev.109,1492(1958).
Andersonmodel-IntroductionByP.W.Andersonin1958[1]当前5页,总共24页。Andersonmodel-IntroductionIn1983and1984Johnextendedthelocalizationconceptsuccessfullytotheclassicalwaves,suchaselasticwaveandopticalwave[1].Followingthepreviousexperimentalwork,TalSchwartzetal.realizedtheAndersonlocalizationwithdisorderedtwo-dimensionalphotoniclattices[2].[1]JohnS,SompolinskyHandStephenMJ1983Phys.Rev.B275592;JohnSandStephenMJ1983286358;JohnS1984Phys.Rev.Lett.
532169[2]SchwartzTal,BartalGuy,FishmanShmuelandSegevMordechai2007Nature
44652当前6页,总共24页。Andersonmodel-openproblemsAbrahansetal.’sscalingtheoryforlocalizationin1979[1](3000citations,oneofthemostimportantpapersincondensedmatterphysics)
Predictions(1)nometal-insulatortransitionin2ddisorderedsystemsSupportedbyexperimentsinearly1980s.
(2)(dephasingtime)ResultsofJ.J.Linin1987[2]
[1]E.Abrahans,P.W.Anderson,D.C.LicciardelloandT.V.Ramakrisbnan,Phys.Rev.Lett.42,673(1979)[2]J.J.LinandN.Giorano,Phys.Rev.B35,1071(1987);J.J.LinandJ.P.Bird,J.Phys.:Condes.Matter14,R501(2002).
当前7页,总共24页。ResultsofJ.J.Linin1987[2]dephasingtime当前8页,总共24页。WorkofHuiXuetal.onsystemswithcorrelateddisorder:刘小良,徐慧,等,物理学报,55(5),2493(2006);刘小良,徐慧,等,物理学报,55(6),2949(2006);徐慧,等,物理学报,56(2),1208(2007);徐慧,等,物理学报,56(3),1643(2007);马松山,徐慧,等,物理学报,56(5),5394(2007);马松山,徐慧,等,物理学报,56(9),5394(2007)。当前9页,总共24页。Andersonmodel-newpointsofview1。CorrelateddisorderCorrelationanddisorderaretwoofthemostimportantconceptsinsolidstatephysicsPower-lawcorrelateddisorderGaussiancorrelateddisorder2。Entanglement[1]:anindexformetal-insulator,localization-delocalizationtransition”entanglementisakindofunlocalcorrelation”(MPLB19,517,2005).Entanglementofspinwavefunctions:fourstatesinonesite:0spin;1up;1down;1upand1downEntanglementofspatialwavefunctions(spinlessparticle):twostates:occupiedorunoccupiedMeasuresofentanglement:vonNewmannentropyandconcurrence[1]HaibinLiandXiaoguangWang,Mod.Phys.Lett.B19,517(2005);JunpengCao,GangXiong,YupengWang,X.R.Wang,Int.J.Quant.Inform.4,705(2006).HefengWangandSabreKais,Int.J.Quant.Inform.4,827(2006).
当前10页,总共24页。Andersonmodel-newpointsofview3.newapplications(1)quantumchaos(2)electrontransportinDNAchainsTheimportanceoftheproblemoftheelectrontransportinDNA[1](3)pentacene[2](并五苯)MolecularelectronicsOrganicfield-effect-transistorspentacene:layeredstructure,2DAndersonsystem[1]R.G.Endres,D.L.CoxandR.R.P.Singh,Rev.Mod.Phys.76,195(2004);StephanRoche,Phys.Rev.Lett.91,108101(2003).[2]M.UngeandS.Stafstrom,SyntheticMetals,139(2003)239-244;J.Cornil,J.Ph.CalbertandJ.L.Bredas,J.Am.Chem.Soc.,123,1520-1521(2001).
DNAstructure当前11页,总共24页。Entanglementinone-dimensionalAndersonmodelwithlong-rangecorrelateddisorder
one-dimensionalnearest-neighbortight-bindingmodelConcurrence:vonNeumannentropy
当前12页,总共24页。Left.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.Right.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationfor=3.0andatthebiggerWrange.Ajumpingfromtheupperbandtothelowerbandisshown
当前13页,总共24页。2DentanglementMethod:takingthe2Dlatticeas1Dchain[1]LongyanGongandPeiqingTong,Phys.Rev.E74(2006)056103.;Phys.Rev.A71,042333(2005).
Quantumsmallworldnetworkin[1]squarelattice当前14页,总共24页。Left.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.Right.TheaveragevonNewmannentropyoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.当前15页,总共24页。Lonczosmethod当前16页,总共24页。EntanglementinDNAchainguanine(G),adenine(A),cytosine(C),thymine(T)QusiperiodicalmodelR-Smodeltogeneratethequsiperiodicalsequencewithfourelements(G,C,A,T).Theinflation(substitutions)ruleisG→GC;C→GA;A→TC;T→TA.StartingwithG(thefirstgeneration),thefirstseveralgenerationsareG,GC,GCGA,GCGAGCTC,GCGAGCTCGCGATAGA∙∙∙.LetFitheelement(site)numberoftheR-Ssequenceintheithgeneration,wehaveFi+1=2Fifori>=1.Sothesitenumberofthefirstseveralgenerationsare1,2,4,8,16,∙∙∙,andforthe12thgeneration,thesitenumberis2048.当前17页,总共24页。TheaverageconcurrenceoftheAndersonmodelfortheDNAchainasthefunctionofsitenumber.Theresultsarecomparedwiththeuncorrelateduniformdistributioncase.
当前18页,总共24页。SpinEntanglementofnon-interactingmultipleparticles:Green’sfunctionmethodFinitetemperaturetwobodyGreen’sfunctionOneparticledensitymatrixandOnebodyGreen’sfunctionTwoparticledensitymatrixwhere,HFapprox.当前19页,总共24页。
Ifandwhere&whereGeneralizedWernerStatethenInbasisSeparabilitycriterion=PPT=alwayssatisfiedsince当前20页,总共24页。ConductanceandmagnetoconductanceoftheAndersonmodelwithlong-rangecorrelateddisorder(1)Staticconductanceofthetwo-dimensionalquantumdotswithlong-rangecorrelateddisorder
Idea:thedistributionfunctionoftheconductanceinthelocalizedregime1d:clearGaussian2d:unclearMethodtocalculatingtheconductance:Green’sfunctionandKuboformula当前21页,总共24页。Fig.1Fig.2aFig.2b当前22页,总共24页。Fig.1ConductanceasthefunctionofFermienergyforthesystemswithpower-lawcorrelatedd
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