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《Phys. Rev. Lett. 67, 2405–2409 (1991) Scaling properties of localization in random band matrices A σ-model approach》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、VOLUME6728OCTOBER1991NUMBER18ScalingPropertiesofLocalizationinRandomBandMatrices:Ao-ModelApproach'andAlexanderD.MirlinYanV.Fyodorov'UniversitatGesamthochschuleEssen,D-4300Essen1,GermanyLeningradNuclearPhysicsInstitute,188350Gatchina,LeningradDistrict,U.S.S.R.(Received21M
2、ay1991)Wereducearandom-band-matrix(RBM)problemtoaone-dimensional,nonlinear,supersymmetric,nmodel.Thisreductionbecomesexactinthelimitb~,bbeingtheeffectivebandwidth.Weprovethatb/N,Nbeingthematrixsize,istherelevantscalingparameter.Whenthemeanvalueofdiagonalelementsincreases
3、linearlyalongthediagonalanextrascalingparameterarises.Theseconclusionsareinagreementwithrecentnumericalresults.PACSnumbers:05.45.+b,72.15.RnAmongotherensemblesofrandommatricesthatofofsuchaparameterwerepresentedin[6,7].Inthere-bandmatricesisunderintensiveinvestigationatpr
4、esent.centpaper[7],anotherclassofRBM(thatwiththeRandombandmatrices(RBM)wereclaimedtobemeanvalueofdiagonalelementslinearlyincreasingalongrelevantfortheexplanationofpropertiesofquantumsys-thediagonal)wasconsidered.Itturnedoutthatanextratemswhoseclassicalcounterpartsdisplay
5、chaoticbehav-scalingparameterenterstheproblem.ior[1].Thekickedrotatorshouldbementionedasagen-Incontrasttonumerouscomputerinvestigationsofericexample[2].Besides,RBMariseinthecourseofin-RBM,analyticalresultsareratherscarce.Besidesthevestigationoftheconductancefluctuationso
6、fthindisor-exactlysolublecaseoftridiagonalmatrices[8],theonlyderedslabsbyatransfer-matrixmethod[3].provenpropertyisthevalidityoftheWignersemicirclePhysicalapplicationsofRBMdictatetheconcentrationlawforthedensityofstates(DOS)whenthebandwidthofinterestonlocalizationpropert
7、iesoftheireigenvectors.bincreaseswiththematrixsizeNasbtx:N~,P)0[9].Whenthebandwidthbissu%cientlysmallalleigenvec-Inthepresentpaperweperformtheanalyticalinvesti-torsarelocalizedandeigenvaluesturnouttobenon-gationoftheRBMpropertieswithintheframeworkofcorrelated.Thisisthein
8、trinsicpropertyofspectraofthesupersymmetricapproach.Thismethodprovedtobequantumsystemsintegrableinthecl
