Distribution of proper delay times in quantum chaotic scattering A crossover from ideal to

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1、Distributionofproperdelaytimesinquantumchaoticscattering:AcrossoverfromidealtoweakcouplingHans-J¨urgenSommers1,DmitryV.Savin1,2,andValentinV.Sokolov21FachbereichPhysik,Universit¨at-GHEssen,45117Essen,Germany2BudkerInstituteofNuclearPhysics,630090Novosibirsk,Russia(

2、Received8May2001;published8August2001:Phys.Rev.Lett.87,094101(2001))Theprobabilitydistributionoftheproperdelaytimesduringscatteringonachaoticsystemisderivedintheframeworkoftherandommatrixapproachandthesupersymmetrymethod.Theresultobtainedisvalidforanarbitrarynumber

3、ofscatteringchannelsaswellasarbitrarycouplingtotheenergycontinuum.Thecaseofstatisticallyequivalentchannelsisstudiedindetail.Inparticular,thesemiclassicallimitofinfinitenumberofweakchannelsispaidappreciableattention.PACSnumbers:05.45.Mt,03.65.Nk,24.60.-k,73.23.-bThet

4、emporalaspectofcollisionandtransportphe-theproperdelaytimes.Usingthenthemethodofor-nomenahas,startingwiththepioneeringworks[1,2],re-thogonalpolynomialstheycalculatedalsothedensityofpeatedlyattractedattention.Analysisofthedurationproperdelaytimes.Thesefindingsreceive

5、dlaterexperi-ofaprocessgivesaninterestingandimportantinforma-mentallyrelevantapplicationstoquantumdots[22]andtioncomplementarytothatdeliveredbytheenergyrep-opticsofrandommedia[23].However,alltheresultsareresentation.Thetemporalapproachbecomesespeciallyrestrictedtot

6、hecaseofperfectcouplingtothecontin-elucidatinginthecasesofchaoticresonancescatteringuum(alltransmissioncoefficientsareequalto1).andtransportindisorderedmediawhenmanycompli-InthisLetterweshowthatrepresentation(1)allowscatedlong-livedintermediatestatesareinvolved[3–16]

7、;ustoextendatleastpartoftheresultsmentionedabovesee[10,17]forrecentreviews.tothecaseofarbitrarycoupling.Namely,wecalculateThedelayofanalmostmonochromaticwavepackettheprobabilitydistributionoftheproperdelaytimesqcduringanM-channelprocessisconventionallydescribedbyth

8、eM×MWigner-SmithmatrixQ=−i¯hS†∂S/∂E,1XM1PM(q)=hδ(q−qc)i=ImG(q−i0),(2)withSbeingthescatteringmatrixatthecollisionenergyMπc=1E.Intheresonancescatte