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1、Thirdordercorrectiontolocalizationinatwo-leveldrivensystemMarcoFrasca∗ViaErasmoGattamelata,300176Roma(Italy)(Dated:February6,2008)AbstractAgeneralresultispresentedonthelackofsecondordercorrectionsandontheformoftheleadingorderFloquetquasi-energiesinthehig
2、h-frequencyapproximationforatwo-leveldrivensystem.Then,byaperturbativeapproachinthehigh-frequencyapproximationthatusesdualDysonseriesandrenormalizationgrouptechniques[M.Frasca,Phys.Rev.B68,165315(2003)],weobtainathirdordercorrectionforasinusoidaldrivingfi
3、eldthatisthesameobtainedbyBarataandWreszinski[Phys.Rev.Lett.84,2112(2000)],confirmingtheirresultthatlocalizationdeviatesfromthezerosofthezero-thorderBesselfunctionwhenhigherordertermsaretakenintoaccount.Threedifferentexpressionsforthiscorrectionarecompared
4、.Animportantconsequenceofthisresultisthatgivescompletesupporttothecorrectnessofbothmethods.Finally,thelimitationofhigh-frequencyapproximationsispresentedbycomparisonwithnumericalresultsforasinusoidaldrivingfield.PACSnumbers:72.20.Ht,73.40.Gk,03.67.LxarXiv
5、:cond-mat/0404692v3[cond-mat.mes-hall]18Nov20041InarecentpaperbyBarataandWreszinski(BW)1anewmethodtosolveperturbativelythedriventwo-levelsystemwaspresented.Theseauthorsshowedthatathirdordercorrec-tion,forthecaseofasinusoidaldrivingfield,appearstochangethe
6、leadingorderFloquetquasienergies,inthelimitoflargefrequency,insuchawaytomodifythenaiveresultthatonehaslocalizationinthetwo-levelsystematthezerosofthezero-thorderBesselfunction.Thisanalyticalresultisinagreement,toacertainextentaswewillsee,withaworkbyCreffie
7、ldaboutthecrossingmanifoldsofthelocalizationpointsinthismodel2,3.AdifferentworkbyPlatero,BrandesandAguado4showedthatanalyticalandnumericalresultsagreefairlywelltakingintoaccounttheresultbyBarataandWreszinski.Thequestionofhigherordercorrectionsisarelevanto
8、neinviewoftheneedsofworkabletwo-levelsystemstobemanipulatedasqubitinquantumcomputers.Thismeansthatgeneralresultsareimportanttoknowtheproperwaytodriveatwo-levelsystemforsuchaims.Inthispaperwepresentaseveralresultsonhigheror