资源描述:
《Third order correction to localization in a two-level driven system》由会员上传分享,免费在线阅读,更多相关内容在行业资料-天天文库。
1、Thirdordercorrectiontolocalizationinatwo-leveldrivensystemMarcoFrasca∗ViaErasmoGattamelata,300176Roma(Italy)(Dated:February6,2008)AbstractAgeneralresultispresentedonthelackofsecondordercorrectionsandontheformoftheleadingorderFloquetquasi-energiesinthehigh-freque
2、ncyapproximationforatwo-leveldrivensystem.Then,byaperturbativeapproachinthehigh-frequencyapproximationthatusesdualDysonseriesandrenormalizationgrouptechniques[M.Frasca,Phys.Rev.B68,165315(2003)],weobtainathirdordercorrectionforasinusoidaldrivingfieldthatisthesame
3、obtainedbyBarataandWreszinski[Phys.Rev.Lett.84,2112(2000)],confirmingtheirresultthatlocalizationdeviatesfromthezerosofthezero-thorderBesselfunctionwhenhigherordertermsaretakenintoaccount.Threedifferentexpressionsforthiscorrectionarecompared.Animportantconsequenceo
4、fthisresultisthatgivescompletesupporttothecorrectnessofbothmethods.Finally,thelimitationofhigh-frequencyapproximationsispresentedbycomparisonwithnumericalresultsforasinusoidaldrivingfield.PACSnumbers:72.20.Ht,73.40.Gk,03.67.LxarXiv:cond-mat/0404692v3[cond-mat.mes
5、-hall]18Nov20041InarecentpaperbyBarataandWreszinski(BW)1anewmethodtosolveperturbativelythedriventwo-levelsystemwaspresented.Theseauthorsshowedthatathirdordercorrec-tion,forthecaseofasinusoidaldrivingfield,appearstochangetheleadingorderFloquetquasienergies,intheli
6、mitoflargefrequency,insuchawaytomodifythenaiveresultthatonehaslocalizationinthetwo-levelsystematthezerosofthezero-thorderBesselfunction.Thisanalyticalresultisinagreement,toacertainextentaswewillsee,withaworkbyCreffieldaboutthecrossingmanifoldsofthelocalizationpoin
7、tsinthismodel2,3.AdifferentworkbyPlatero,BrandesandAguado4showedthatanalyticalandnumericalresultsagreefairlywelltakingintoaccounttheresultbyBarataandWreszinski.Thequestionofhigherordercorrectionsisarelevantoneinviewoftheneedsofworkabletwo-levelsystemstobemanipula
8、tedasqubitinquantumcomputers.Thismeansthatgeneralresultsareimportanttoknowtheproperwaytodriveatwo-levelsystemforsuchaims.Inthispaperwepresentaseveralresultsonhigheror