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1、weekendingPRL106,221601(2011)PHYSICALREVIEWLETTERS3JUNE2011HolographicJosephsonJunctionsGaryT.Horowitz,JorgeE.Santos,andBensonWayDepartmentofPhysics,UniversityofCalifornia,SantaBarbara,California93106-4030,USA(Received31January2011;published3June2011)Weconstructagravitatio
2、naldualofaJosephsonjunction.Calculationsonthegravitysidereproducethestandardrelationbetweenthecurrentacrossthejunctionandthephasedifferenceofthecondensate.Wealsostudythedependenceofthemaximumcurrentonthetemperatureandsizeofthejunctionandreproducefamiliarresults.DOI:10.1103
3、/PhysRevLett.106.221601PACSnumbers:11.25.Tq,04.70.Bw,74.20.zIntroduction.—Oneofthemostremarkableresultsc¼c~=q,A¼A=q~andtakeq!1,keepingc~andA~toemergefromstringtheoryisgauge-gravitydualityfixed.Inthislimit,thebackreactionofthesefieldsonthe[13]theequivalencebetweenatheoryofgr
4、avityandametriccanbeignored.Therefore,wecanfixthemetricnongravitationaltheory.Thisequivalenceiscalledholo-backgroundtobetheAdSplanarSchwarzschildblackgraphicsincethenongravitationalsystemlivesinalowerhole:dimensionalspacethantheonewithgravity.Inrecentyearsthisdualityhasbeen
5、successfullyappliedtocon-dr2densedmattersystems[4,5].Inparticular,agravitationalds2¼fðrÞdt2þþr2ðdx2þdy2Þ;dualofasuperconductorhasbeenfound[6,7].InthisfðrÞ(2.2)Letter,weextendthisconstructiontoobtainagravitationalr2r3fðrÞ¼10;dualofaJosephsonjunction.23LrAJosephsonjuncti
6、on[8]consistsoftwosuperconduc-torsseparatedbyaweaklink.Ifthelinksupportsaphasedifferencebetweenthecondensateofthetwowherer0istheblackholehorizonradiusandLtheAdSsuperconductors,therewillbeacurrentacrossthejunctionlengthscale.ThetemperatureofthisblackholeisgivenbygivenbyT¼3r
7、0.4L2ThissimplemodelhasbeenshowntoprovideadualJ¼Jmaxsin
:(1.1)descriptionofasuperconductor[7].Asaconsequenceofascalingsymmetry,thecriticaltemperatureTcofthesuper-Thiscurrentexistswithnoappliedvoltage.Thereareconductorisproportionaltothechemicalpotential.severaltypesofJos
8、ephsonjunctionsdependingontheWewillallowthechemicalpotentialtohavespatialde-natureofthisl
