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1、Thirdordercorrectiontolocalizationinatwo-leveldrivensystemMarcoFrasca∗ViaErasmoGattamelata,300176Roma(Italy)(Dated:February6,2008)AbstractAgeneralresultispresentedonthelackofsecondordercorrectionsandontheformoftheleadingorderFloquetquasi-energiesinthehigh-freq
2、uencyapproximationforatwo-leveldrivensystem.Then,byaperturbativeapproachinthehigh-frequencyapproximationthatusesdualDysonseriesandrenormalizationgrouptechniques[M.Frasca,Phys.Rev.B68,165315(2003)],weobtainathirdordercorrectionforasinusoidaldrivingfieldthatisthe
3、sameobtainedbyBarataandWreszinski[Phys.Rev.Lett.84,2112(2000)],confirmingtheirresultthatlocalizationdeviatesfromthezerosofthezero-thorderBesselfunctionwhenhigherordertermsaretakenintoaccount.Threedifferentexpressionsforthiscorrectionarecompared.Animportantconseq
4、uenceofthisresultisthatgivescompletesupporttothecorrectnessofbothmethods.Finally,thelimitationofhigh-frequencyapproximationsispresentedbycomparisonwithnumericalresultsforasinusoidaldrivingfield.PACSnumbers:72.20.Ht,73.40.Gk,03.67.LxarXiv:cond-mat/0404692v3[cond
5、-mat.mes-hall]18Nov20041InarecentpaperbyBarataandWreszinski(BW)1anewmethodtosolveperturbativelythedriventwo-levelsystemwaspresented.Theseauthorsshowedthatathirdordercorrec-tion,forthecaseofasinusoidaldrivingfield,appearstochangetheleadingorderFloquetquasienergi
6、es,inthelimitoflargefrequency,insuchawaytomodifythenaiveresultthatonehaslocalizationinthetwo-levelsystematthezerosofthezero-thorderBesselfunction.Thisanalyticalresultisinagreement,toacertainextentaswewillsee,withaworkbyCreffieldaboutthecrossingmanifoldsoftheloca
7、lizationpointsinthismodel2,3.AdifferentworkbyPlatero,BrandesandAguado4showedthatanalyticalandnumericalresultsagreefairlywelltakingintoaccounttheresultbyBarataandWreszinski.Thequestionofhigherordercorrectionsisarelevantoneinviewoftheneedsofworkabletwo-levelsyste
8、mstobemanipulatedasqubitinquantumcomputers.Thismeansthatgeneralresultsareimportanttoknowtheproperwaytodriveatwo-levelsystemforsuchaims.Inthispaperwepresentaseveralresultsonhigheror
