Entropy flow through near-critical quantum junctions

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1、Entropyflowthroughnear-criticalquantumjunctionsDanielFriedan∗DepartmentofPhysicsandAstronomy,Rutgers,TheStateUniversityofNewJersey,Piscataway,NewJersey08854-8019,USAandTheScienceInstitute,TheUniversityofIceland,Reykjavik,Iceland(Dated:May3,2005)Thisisthecontinuationofcond-mat/0505084.Elementaryformu

2、lasarederivedfortheflowofentropythroughacircuitjunctioninanear-criticalquantumcircuit,basedonthestructureoftheenergy-momentumtensoratthejunction.Theentropicadmittanceofanear-criticaljunctioninabulk-criticalcircuitisexpressedintermsofcommutatorsofthechiralentropycurrents.Theentropicadmittanceatlowfre

3、quency,dividedbythefrequency,givesthechangeofthejunctionentropywithtemperature—theentropic“capacitance”.Asanexample,andasacheckontheformalism,theentropicadmittanceiscalculatedexplicitlyforjunctionsinbulk-criticalquantumIsingcircuits(freefermions,masslessinthebulk),intermsofthereflectionmatrixoftheju

4、nction.Thehalf-bitofinformationcapacityperendofcriticalIsingwireisre-derivedbyintegratingtheentropic“capacitance”withrespecttotemperature,fromT=0toT=∞.PACSnumbers:03.67.-a,05.30.-d,05.60GgI.SUMMARYThispapercontinuestheelementaryinvestigationofentropyflowinnear-criticalquantumcircuitsbeguninRef.1.The

5、entropycurrentoperator,whichisjusttheenergycurrentdividedbythetemperature,j(x,t)=kβTx(x,t),isStusedtoanalyzetheflowofentropythroughthegeneraljunctioninanear-criticalquantumcircuit,especiallywhenthequantumwiresarecriticalinthebulksothattheonlydeparturefromcriticalityisinthejunction.Entropyflowsinandou

6、tofthejunctioninresponsetochangesintheentropicpotentialsinthewires,whicharejustthetemperaturedropsinthewires.Thelinearresponsecoefficientfortheentropycurrentistheentropicadmittanceofthejunction.Thejunctionentropy,s(T),isthe“charge”inthejunction.Theentropic“capacitance”—thetemperaturederivative,ds/dT—

7、isextractedfromthelowfrequencylimitoftheentropicadmittance.Theinformationcapacityofthejunction,s(∞)−s(0)isfoundbyintegratingwithrespecttoT.Thejunctionentropyitselfneedsaglobalcalculation,butchangesinthejunc