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One-andtwo-dimensionalAndersonmodelwithlong-rangecorrelated-disorder一维和二维关联无序安德森模型

One-andtwo-dimensionalAndersonmodelwithlong-rangecorrelated-disorderAndersonmodel-IntroductionEntanglementin1D2DEntanglement2Dconductance2Dtransmission2DmagnetoconductanceAndersonmodel-IntroductionWhatisadisorderedsystem?Nolong-rangetranslationalorderTypesofdisorder

(a)crystal(b)Componentdisorder(c)positiondisorder(d)topologicaldisorder

diagonaldisorder

off-diagonaldisordercompletedisorderLocalizationprediction:anelectron,whenplacedinastrongdisorderedlattice,willbeimmobile[1]P.W.Anderson,Phys.Rev.109,1492(1958).

Andersonmodel-IntroductionByP.W.Andersonin1958[1]Andersonmodel-IntroductionIn1983and1984Johnextendedthelocalizationconceptsuccessfullytotheclassicalwaves,suchaselasticwaveandopticalwave[1].Followingthepreviousexperimentalwork,TalSchwartzetal.realizedtheAndersonlocalizationwithdisorderedtwo-dimensionalphotoniclattices[2].[1]JohnS,SompolinskyHandStephenMJ1983Phys.Rev.B275592;JohnSandStephenMJ1983286358;JohnS1984Phys.Rev.Lett.

532169[2]SchwartzTal,BartalGuy,FishmanShmuelandSegev

Mordechai2007Nature

44652Andersonmodel-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).

ResultsofJ.J.Linin1987[2]dephasingtimeWorkofHui

Xuetal.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)。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);Junpeng

Cao,GangXiong,YupengWang,X.R.Wang,Int.J.Quant.Inform.4,705(2006).HefengWangandSabreKais,Int.J.Quant.Inform.4,827(2006).

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).

DNAstructureEntanglementinone-dimensionalAndersonmodelwithlong-rangecorrelateddisorder

one-dimensionalnearest-neighbortight-bindingmodelConcurrence:vonNeumannentropy

Left.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.Right.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationfor=3.0andatthebiggerWrange.Ajumpingfromtheupperbandtothelowerbandisshown

2DentanglementMethod:takingthe2Dlatticeas1Dchain[1]LongyanGongandPeiqingTong,Phys.Rev.E74(2006)056103.;Phys.Rev.A71,042333(2005).

Quantumsmallworldnetworkin[1]squarelatticeLeft.TheaverageconcurrenceoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.Right.TheaveragevonNewmannentropyoftheAndersonmodelwithpower-lawcorrelationasthefunctionofdisorderdegreeWandforvarious.Abandstructureisdemonstrated.LonczosmethodEntanglementinDNAchainguanine(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.TheaverageconcurrenceoftheAndersonmodelfortheDNAchainasthefunctionofsitenumber.Theresultsarecomparedwiththeuncorrelateduniformdistributioncase.

SpinEntanglementofnon-interactingmultipleparticles:Green’sfunctionmethodFinitetemperaturetwobodyGreen’sfunctionOneparticledensitymatrixandOnebodyGreen’sfunctionTwoparticledensitymatrixwhere,HFapprox.

Ifandwhere&whereGeneralizedWernerStatethenInbasisSeparabilitycriterion=PPT=alwayssatisfiedsinceConductanceandmagnetoconductanceoftheAndersonmodelwithlong-rangecorrelateddisorder(1)Staticconductanceofthetwo-dimensionalquantumdotswithlong-rangecorrelateddisorder

Idea:thedistributionfunctionoftheconductanceinthelocalizedregime1d:clearGaussian2d:unclearMethodtocalculatingtheconductance:Green’sfunctionandKuboformulaFig.1Fig.2aFig.2bFig.1ConductanceasthefunctionofFermienergyforthesystemswithpower-lawcorrelateddisorder(W=1.5)forvariousexponent.Ther

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