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1、Thirdordercorrectiontolocalizationinatwo-leveldrivensystemMarcoFrasca∗ViaErasmoGattamelata,300176Roma(Italy)(Dated:February6,2008)AbstractAgeneralresultispresentedonthelackofsecondordercorrectionsandontheformoftheleadingorderFloquetquasi-energiesinthehigh-frequencyapproximationforatwo-leveldrivens
2、ystem.Then,byaperturbativeapproachinthehigh-frequencyapproximationthatusesdualDysonseriesandrenormalizationgrouptechniques[M.Frasca,Phys.Rev.B68,165315(2003)],weobtainathirdordercorrectionforasinusoidaldrivingfieldthatisthesameobtainedbyBarataandWreszinski[Phys.Rev.Lett.84,2112(2000)],confirmingthei
3、rresultthatlocalizationdeviatesfromthezerosofthezero-thorderBesselfunctionwhenhigherordertermsaretakenintoaccount.Threedifferentexpressionsforthiscorrectionarecompared.Animportantconsequenceofthisresultisthatgivescompletesupporttothecorrectnessofbothmethods.Finally,thelimitationofhigh-frequencyappr
4、oximationsispresentedbycomparisonwithnumericalresultsforasinusoidaldrivingfield.PACSnumbers:72.20.Ht,73.40.Gk,03.67.LxarXiv:cond-mat/0404692v3[cond-mat.mes-hall]18Nov20041InarecentpaperbyBarataandWreszinski(BW)1anewmethodtosolveperturbativelythedriventwo-levelsystemwaspresented.Theseauthorsshowedth
5、atathirdordercorrec-tion,forthecaseofasinusoidaldrivingfield,appearstochangetheleadingorderFloquetquasienergies,inthelimitoflargefrequency,insuchawaytomodifythenaiveresultthatonehaslocalizationinthetwo-levelsystematthezerosofthezero-thorderBesselfunction.Thisanalyticalresultisinagreement,toacertain
6、extentaswewillsee,withaworkbyCreffieldaboutthecrossingmanifoldsofthelocalizationpointsinthismodel2,3.AdifferentworkbyPlatero,BrandesandAguado4showedthatanalyticalandnumericalresultsagreefairlywelltakingintoaccounttheresultbyBarataandWreszinski.Thequestionofhigherordercorrectionsisarelevantoneinviewof
7、theneedsofworkabletwo-levelsystemstobemanipulatedasqubitinquantumcomputers.Thismeansthatgeneralresultsareimportanttoknowtheproperwaytodriveatwo-levelsystemforsuchaims.Inthispaperwepresentaseveralresultsonhigheror