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1、Thirdordercorrectiontolocalizationinatwo-leveldrivensystemMarcoFrasca∗ViaErasmoGattamelata,300176Roma(Italy)(Dated:February6,2008)AbstractAgeneralresultispresentedonthelackofsecondordercorrectionsandontheformoftheleadingorderFloquetquasi-energiesinthehigh-frequencyapproximationforatw
2、o-leveldrivensystem.Then,byaperturbativeapproachinthehigh-frequencyapproximationthatusesdualDysonseriesandrenormalizationgrouptechniques[M.Frasca,Phys.Rev.B68,165315(2003)],weobtainathirdordercorrectionforasinusoidaldrivingfieldthatisthesameobtainedbyBarataandWreszinski[Phys.Rev.Lett.
3、84,2112(2000)],confirmingtheirresultthatlocalizationdeviatesfromthezerosofthezero-thorderBesselfunctionwhenhigherordertermsaretakenintoaccount.Threedifferentexpressionsforthiscorrectionarecompared.Animportantconsequenceofthisresultisthatgivescompletesupporttothecorrectnessofbothmethods
4、.Finally,thelimitationofhigh-frequencyapproximationsispresentedbycomparisonwithnumericalresultsforasinusoidaldrivingfield.PACSnumbers:72.20.Ht,73.40.Gk,03.67.LxarXiv:cond-mat/0404692v3[cond-mat.mes-hall]18Nov20041InarecentpaperbyBarataandWreszinski(BW)1anewmethodtosolveperturbativelyt
5、hedriventwo-levelsystemwaspresented.Theseauthorsshowedthatathirdordercorrec-tion,forthecaseofasinusoidaldrivingfield,appearstochangetheleadingorderFloquetquasienergies,inthelimitoflargefrequency,insuchawaytomodifythenaiveresultthatonehaslocalizationinthetwo-levelsystematthezerosofthez
6、ero-thorderBesselfunction.Thisanalyticalresultisinagreement,toacertainextentaswewillsee,withaworkbyCreffieldaboutthecrossingmanifoldsofthelocalizationpointsinthismodel2,3.AdifferentworkbyPlatero,BrandesandAguado4showedthatanalyticalandnumericalresultsagreefairlywelltakingintoaccountther
7、esultbyBarataandWreszinski.Thequestionofhigherordercorrectionsisarelevantoneinviewoftheneedsofworkabletwo-levelsystemstobemanipulatedasqubitinquantumcomputers.Thismeansthatgeneralresultsareimportanttoknowtheproperwaytodriveatwo-levelsystemforsuchaims.Inthispaperwepresentaseveralresul
8、tsonhigheror