The Knight of the Quantum On the Contribution of D.I. Blokhintsev to Quantum Physics

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A.L.Kuzemsky

JointInstituteforNuclearResearch,Dubna,Russiakuzemsky@theor.jinr.ru;http://theor.jinr.ru/˜kuzemsky

Abstract

AconcisesurveyofthecontributionofD.I.Blokhintsevtothequantumphysics,includingsolidstatephysics,physicsofmetals,surfacephysics,statisticalphysicsandopticsisgiven.Theseachievementshavebeenconsideredinthecontextofmoderndevelopmentofthesefieldsofphysics.

ThenameofCorrespondingMemberoftheAcademyofSciencesoftheUSSRD.I.Blokhintsev(January11,1908–January27,1979)iswidelyknowninRussiaandabroad.Hisbooksarebeingrepublished;informationonhisbiographyandhisscientificheritagecanbefoundinmultiplepapersandcollectionsofpapers.However,formanyscientists,hisnameisrelatedmainlytohisworksinthefieldofatomicandnuclearphysics,appliedacoustics,participationinthecreationofthefirstnuclearpowerstationinObninsk,reactorconstruction,andmultiplestudiesinhighenergyandelementaryparticlephysics.Itisnotsowellknownthatatfirsthewrotesomequiteinterestingandimportantworksinthefieldofquantumsolidstatephysicsandstatisticalphysics.Inthebeginningofhisdistin-guishedacademiccareer[1,2],D.I.Blokhintsevhasworkedinthefieldofquantumsolidstatephysicsandstatisticalphysics,aswellasinthefieldofquantumphysics[1].Theaimofmytalkistorecallthesequiteinterestingandimportantworksandcorrelatethemwithcorrespondingmoderndirectionsincondensedmatterphysicsandquantumphysics[3].D.I.BlokhintseventeredthePhysicsFacultyofMoscowStateUniversityin1926.AtthattimeL.I.MandelstamwastheheadoftheDepartmentoftheoreticalphysicsandopticsandI.E.TammwasprofessoroftheoreticalphysicsofthatDepartment.Blokhintsevcon-sideredL.I.Mandelstam,S.I.VavilovandI.E.Tammhisteachers.I.E.TammbecomehisPh.D.promotorinpostgraduatestudies.Thus,Blokhintsev’sstudentyearsbroughthimgreatandfruitfulexperienceincommunicating,atlecturesandinlaboratories,withbrilliantandinterestingrepresentativesofphysicalsciencesofthetime.BlokhintsevwascertainlyinfluencedstronglybyMandelstamandlearnedalotfromhim,inparticular,hisbreadthofviewsonphysicsasanindivisiblescience,lecturingskills,understandingtheimportanceofascientificschool,organizationofscience,etc.Aswasnotedlater,”LecturesandseminarsgivenbyMandelstamattheuniversityin1925-1944wereofspecialimpor-tance.Theyweredevotedtoawidefieldofthemosttopicalproblemsinphysicsinwhichthelecturerdeliveredanextremelydeepanalysisofthemodernstateoftheartwithoutconcealingexistingdifficulties,andheoutlinedoriginalsolutionstoverycomplexproblems.Theselecturesattractedawideaudienceofphysicistsofvariousagesandranksfromall

partsofMoscow.”Mandelstamdeliveredhisfamouslecturesontheprinciplesofquantummechanics(thetheoryofindirectmeasurements)inspringof1939.Heintendedtoreadaseriesoflecturesontheconnectionofthemathematicaltoolsofquantummechanicsanditsstatisticalinterpretation,causality,etc.,asacontinuationoftheselectures;thebasisofthisseriesoflectureswassupposedtobethefamousbookwrittenbyJ.vonNeumann.Later,thisprogramwasrealizedbyBlokhintsev.

Itwastimewhenquantummechanicshadacquiredacertainmaturity[4].InthebookbyGurney[5],alsoreferredtoinBlokhintsev’sworks,quantummechanicsischaracterizedasanewlanguageofphysicsandchemistry.”Theprogramofquantummechanicsincludesnomoreandnolessthanthereconsiderationofatomicandmolecularphysicsintheiren-tiretyonthebasisofnewlawsofbehaviorofparticlesfollowingfromquantummechanics”.Blokhintsevjoinedtherealizationofaprogramofreconsiderationofatomicandsolidstatephysicsintheirentiretyonthebasisofnewquantumphysicswithenthusiasm.Ashelaterrecollected,”Duringthatperiod(1927-1929),newquantummechanicsoriginatedandgreatcapabilitiesintheapplicationofthisnewphysicalconceptandnewmethodsofcalculationofvariousatomicphenomenawerefound”[1].Atthattime,solidstatephysics,inpar-ticular,thetheoryofmetals,attractedgreatattention.In1932,thework”TemperatureDependenceofthePhotoeffectonPureMetals”ofD.I.Blokhintsevwaspublished.Thenextpaperwas”TheWorkFunctionofElectronsfromMetals”(1933)(jointlywithI.E.Tamm).Inthemonograph[6]thisstudybyTammandBlokhintsevwascitedtogetherwithotherbasicworksontheproblem.Thus,fromtheverybeginning,hisworkswereatthehighestlevelofquality.TheearlyworksofD.I.Blokhintsevhavemanifestedalsohistalentsofclearvividpresentationofthesubject,transparentstyle,concreteness,theabilitytopointoutmostsignificantthingsand,mostimportant,emphasisonthephysicalmeaning.InalargeworkbyBlokhintsevin1933”TheoryofElectronMotioninaCrys-talLattice”,theF.Blochtheoryofmotionoftightbindingelectronswasgeneralizedforthemanybandscaseandfortheelectronmotioninacrystalwhichisboundedbysur-face.Thenextworkwasthepaper”TheoryofAnomalousMagneticandThermoelectricEffectsinMetals”(1933)coauthoredwithL.W.Nordheim(19-1985).Inthiswork,theconsistenttheoryofthermoelectricandgalvanomagneticeffectsinmetalswasconstructed.Unlikeearlierworks,thecaseofs−pbandmetalswasconsidered.Theauthorsstudiedthebehaviorofdivalentmetalsinamagneticfield(ThompsonandHalleffects).Tomaketheirequationscompact,BlokhintsevandNordheimintroducedanewnotion,thetensorofreciprocaleffectivemasses.InthebookofMottandJones[6],thepriorityofBlokhintsevandNordheiminthecreationofthisfundamentalnotionwasestablished.TheachievementmadebyBlokhintsevandNordheimwasthattheyshowedthattheconceptofeffectivemasswasmuchmoregeneralandworkablethanhadbeenassumedbeforeandforthefirsttimedemonstratedthetensorcharacteroftheeffectivemassbyconsideringthebehavioroftheelectroninexternalfields.Itturnedoutthatthenotionofeffectivemassisextremelyusefulinthetheoryofconductivityandotherfieldsofsolidstatephysics,nuclearphysics,etc.Theconceptofeffectivemassbecamewidelyapplied,especiallyinsemiconductorphysicsandthephysicsofsemiconductordevices,thepolarontheory,semiconductorsuperlattices,microelectronicsandphysicsofnanostructures.

AfewwordshouldbesaidaboutBlokhintsev’scoauthorLotarWolfgangNordheim(19-1985).NordheimbelongedtotheGettingenschooloftheoreticalphysics.HewasaPhDstudentwithM.Born,andafterdefendinghisPhDthesisin1923,hisassistantandcol-2

leaguetill1933.Allhisworksaremarkedbybrighttalentanddeepinsightintoaproblem.InJammer’sbook[4],thefollowingfactisgiven:”Inautumnof1926,Hilbertbegansys-tematicstudiesofthemathematicalprinciplesofquantummechanics.LotarWolfgangNordheim,Born’sformerstudent,andthe23-year-oldJohnvonNeumannhelpedhiminthesestudies.Hilbertalsogavelecturesonthemathematicalprinciplesofquantumtheory,whichwerepublishedinshorterforminthespringof1927.”Nordheimworkedsuccess-fullyintheapplicationofquantummechanicstostatisticalphysicsandsolidstatephysics.Hegaveasuccessfuldescriptionoftheelectronworkfunctioninmetals,thermoelectronemission,electronkineticsinmetalsandalloys,etc.ThankstoagrantfromtheRockfellerFoundation,NordheimvisitedMoscowin1933asaninvitedprofessortoMSU.HisstudieswerequiteclosetothoseperformedbytheTamm’sgroup.ItwasduringthatvisitthatheperformedhisjointworkwithBlokhintsev.

In1933,Blokhintsevpublished”TheoryoftheStarkEffectsinaTime-DependentField”.InthispaperBlokhintsevshowedthattheatomiclevelsmoveunderinfluenceofvariableelectricfield(Starkmodulation).Thepictureoflightscatteringdependsnonlinearlyontheintensityoftheincidentlight.Thisworkwasoneofthefirstinthefieldofphysics,whichwaslattercallednonlinearoptics.

In1934,Blokhintsevpublishedpaperonthetheoryofphosphorescence.Accordingtotheauthor,”AnattemptwasmadetoexplainthephenomenonofphosphorescenceinthesocalledLenardphosphorsonthebasisofquantummechanicalideasoftheelectronmotioninthecrystallattice”[1].Blokhintsevassumedthatdurationofthephosphorescencecanberelatedwiththecapabilityofformationofquasilocalizedelectronicstatesinarealcrystalasaresultofthelocallatticedeformationduetotheintroductionimpurities.Thenhees-timatedthetimeofreciprocalrecombinationofthesestates.Thus,thetheoryoflocalizedstatesmadeitpossibletoqualitatively(and,partially,quantitatively)interpretthebigdurationofthephosphorescence.Thispointofviewwasincludedintextbooksonoptics.ThisandsubsequentworksbyBlokhintsev,inwhichthedetailedtheoryofthekineticsofphosphorescenceinheteropolarcrystalsandthetheoryofdyedcrystalswereconstructed,contributedconsiderablytodeeperunderstandingofthisproblemandshowedoncemorethatthequantummechanicalapproachisindeedthe”newlanguageofphysicsandchem-istry”,providingeffectivedescriptionofphenomenaconsidered”mysterious”inclassicalphysics.ThesameapproachwasusedbyBlokhintsevinthework”QuantumMechanicalTheoryofAdsorption”(1934)(co-authoredwithSh.Shekhter).Thisworkisaveryusefulandclearsurveyoftheproblemasawhole.Thepaperofthesameauthors”LifetimeofParticlesinAdsorbedState”(1934)wasdevotedtothecalculationofthelifetimeofparti-clesintheadsorbedstate.Inthatpaperitwasdemonstratedhowthequantummechanicsprovidesonewiththemicroscopicpictureofphenomenon.Theauthorsobtainedthecor-rectqualitativebehavioroftheaveragelifetimeoftheadsorbedmoleculeonthesurface,whichdemonstratedoncemoretheeffectivenessofthequantummechanicalapproach.In1934,BlokhintsevpresentedhisPh.D.thesistotheInstituteofPhysicsoftheMoscowStateUniversity,entitledSelectedProblemsoftheSolidStateTheory,EspeciallyMetals.Asaresultofthehighlevelofthework,hereceivedadegreeofDoctorofScience.Atthetime,Blokhintsevwas26yearsold.

In1935–1936,Blokhintsevcontinuedhisworkonthetheoryoflightabsorptioninhet-eropolarcrystals,thetheoryofphosphorescence,andthetheoryofdyedcrystals.Itisinterestingtonotethatinthepaper”TheoryofDyedCrystals”(1936),Blokhintsev,in

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certainsense,anticipatedtheconceptofthepolaron,whichwasformulatedlaterbyS.I.Pekar(1917-1985).S.I.Pekarwrotethisstoryinhiswellknownmonograph[7]in1951:”In1936,BlokhintsevattemptedtofindoutinwhichcrystalsautolocalizationofelectronspointedoutbyLandaushouldbeexpectedonthebasisoftheapproximationoftight-bindingelectrons...”.Asiswellknown,S.I.Pekarcoinedtheveryterm,polaron,in1946.Themainideawasthat”excess”electroninioniccrystalpolarizesthecrystallattice;thispolarizationinturninfluencestheelectron,andthisactionisequivalenttotheactionofsomeeffectivepotentialwell.Thedepthofthiswellinsomecrystalsmaybesufficientlylargefordiscreteenergylevelstoexistinit.Localpolarizationcausedbytheelectronisrelatedtothedisplacementofionsfromtheiraverageequilibriumpositions.ThesestatesofthecrystalwiththepolarizationwellinwhichtheelectronislocalizedweretermedpolaronsbyPekar.ThecontributionmadebyBlokhintsevin1936tothisdirectionofresearcheswasmentionedlaterbyafewotherinvestigators.Themainpointwastheformulationoftheproblemofautolocalizedelectronicstatesonthebasisofapproximationoftight-bindingelectrons.Thisapproximation(LCAO)[3]laterbecomewidelyusedincondensedmatterphysics,especiallyforthedescriptionoflocalizedstatesofdifferentnatureanddisorderedsystems.Theinvestigationoflocalizedstatesintheframeworkofthetight-bindingapprox-imationbringedBlokhintsevtothepoint,namelytotheneedtodescribetheinteractionoftheelectronwiththelatticevibrationsaccordinglytothespiritoftight-bindingapprox-imation.Thiswascarriedoutmuchlater(seefordetailsRef.[3]).

In1938,Blokhintsevpreparedhiswork”TheShiftofSpectralLinesCausedbytheInverseActionofaRadiationField”forpublication.HepresenteditataseminarofthePhysicalInstituteoftheAcademyofSciencesoftheUSSR,wherehewasemployed;healsosub-mittedittoZhurnalExperimental’noiiTeoreticheskoiFiziki[JournalofExperimentalandTheoreticalPhysics](ZhTEF).Theworkwasrejectedbytheeditorialboardandpublishedonlyin1958inDubnainacollectionofBlokhintsev’sscientificworksandpapers.ThisworkwasmentionedinthesurveyreportdeliveredbyYa.A.Smorodinskii[8]in1949.Lateron,thefollowingwaswritten[9]:”AlreadyinearlyworksbyBlokhintsev,deepunderstandingoftheessenceofquantummechanics,freshandboldideas,anoriginalwayofthinkingthatforeshadowedthefurtherdevelopmentofphysicswereevident.Typicalinthisrespectwashisworkonthecalculationofthe’shiftofspectrallinescausedbyinverseactionofaradiationfield,’whichinessencecontainedthetheoryoftheLambshift,whichwasthebeginningofquantumelectrodynamics.ItwasreportedattheseminaratthePhysicsIn-stituteoftheAcademyofSciencesoftheUSSRandsubmittedtoZhTEFin1938.TheformulafortheLambshiftobtainedbyBlokhintsevbecamefamous;itdiffersfromtheBetheformulaonlybythenumericalfactoraddedin1948asaresultofultravioletcutoff.Unfortunately,thisimportantdiscoverywasnotpublishedatthattimeinZhTEF.Therewerenootheroutletsforpublication”.Thegenesisofthework”TheShiftofSpectralLinesCausedbytheInverseActionofaRadiationField”wasbestdescribedbyBlokhintsevhimself[1].”Ideliveredtheworkthat,inessence,containedthetheoryoftheLambshiftdiscoveredtenyearslater,ataseminaratthePhysicsInstitute.However,myworkwasnotpublished,sincetheeditorialboardofZhETFreturnedthemanuscriptbecausethecalculationswereconsideredunusual.Ikeptthemanuscript,whichwasstampedbythejournalcertifyingthedateofitsreceipt(February25,1938).IfoundnosupportfrommycolleaguesatthePhysicsInstitute.Therewerenootheroutlets.Thus,thisimportantworkwasnotpublishedinduetime.Themainideaoftheworkfollowedfrommydeepbelief

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thataphysicalvacuumexistedinreality;however,Irefrainedfrompresentingtheaffairinthislight...”.TheLambshiftisindeedrelatedtoquiteremarkableandinterestingeffectsofquantumphysics[10].Lambandhiscolleaguesperformedveryprecise,thorough,andelegantexperimentalstudiesonthedeterminationofthestructureoflevelswithn=2forhydrogen,deuterium,andsinglyionizedhelium.Sincetheenergydifferencefortheselevelsisverysmall,theprobabilityofspontaneoustransitionsturnsouttobenegligible.However,iftheatomisplacedinarotating(oroscillating)magneticfieldwiththecorrespondingfrequency,inducedtransitioncanbeobserved.Thisfrequencycanbeexactlymeasured;itisequaltothedifferenceinenergiesofthetwolevelsdividedbyh¯.ThemeasurementoftherotationfrequencyinLamb’sexperimentsyieldedavalueoftheenergydifferenceoftwolevelswiththesameprincipalquantumnumberinRydbergunits;itisinterestingthatthisdoesnotrequireanypreliminarydataonthePlanckconstanth¯.TheLambshiftismainlydeterminedbythevariationinthe”scale”inwavefunctionsoftheatom,whichareuseduponcalculationofthemathematicalexpectationofcorrespondingexpressions.Blokhint-sevwroteabouthiscalculationsin[1]:”Asaresultofthem,thefollowingexpressionisobtainedforthefrequencyshift:

δω0=k(

e

2

n3

Rlg

󰀁

µc2

errors.Weovercamedifficultiesslowly,sincetherewerenogoodexperimentalresultsatthattime.ThenLambandRetherfordsetupagoodexperiment,andfinally,weobtainedaresultthatagreedwellwithexperimentaldata.IinformedJulianSchwingerandDickFeynman;theyrepeatedthecalculations;however,theirresultsweredifferentfromours,andSchwingerandFeynmanobtainedthesamenumber.Wepostponedpublicationtofindtheerror,spendinghalfayearonit.Meanwhile,LambandKrollpublishedcalculationresultofthesameeffect,whichmoreorlessagreedwithourresult.ThenFeynmancalledmefromIthaca,”Youwereright;Iwaswrong!”Thus,ifwehadhadcouragetopublishourresults,ourpaperwouldhavebeenthefirstonetoexplaintheexperimentperformedbyLambandRetherford.What’sthemoralofthisstory?Youhavetobelieveinwhatyoudo.”

In1939,Blokhintsevpublishedhiswork”HydrodynamicsofanElecrongas”.Inthiswork,thehydrodynamicdescriptionofthesystemofmanyparticles(electrons),i.e.,descriptionintermsofa”reduced”setofvariablescharacterizingthesystem,thecurrentI(x)andtheparticledensityρ(x),wasconsidered.Blokhintsevmaintainedthatsinceamany-particleproblemcouldnotbesolvedexactly,anapproximatesolutionshouldbesought.Itisknownthatanefficientwayforcalculatingtheenergyeigenfunctionsandeigenvaluesistheself-consistentfieldmethod.ThismethodwasfirstdevelopedbyHartreewithouttakingintoaccountelectronexchangeandthenbyFockwiththisexchangetakenintoaccount.Thereexistalargenumberofworksonthismethodbothwithandwithouttheexchangeaccount.BlokhintsevwroteinhisworkthatfromtheverybeginningheusedtheHartree-Fockapproximation,whichassignsanindividualfunctionψk(x)toeachelectronn.Inthisap-proximation,thesystemofelectronsisdescribedbythedensitymatrix.Consideringthedynamicequations(equationsofmotion)forthecurrent,Blokhintsevderivedthe”hydro-dynamic”equationforasystemofmanyparticles(electrons)thatcontainedgasdensitygradientsinthestresstensor.Toobtainclosedexpressions,heusedapproximationschar-acteristicofstatisticalFermi-Thomastheory.Itisknownthatthestatisticalmodeloftheatomdescribestheelectronsoftheatomstatisticallyasanelectrongasatatemperatureofabsolutezero.Themodelyieldsgoodapproximationonlyforatomswithalargenumberofelectrons,althoughithadbeenusedforuptotenelectrons.Forthestatisticalapproach,thedetailsoftheelectronicstructurehadnotbeendescribed;therefore,theapplicationofahydrodynamicdescriptionwasquiterelevant.Followingthespiritofthestatisticalmodeloftheatom,thetotalenergyoftheatomisobtainedfromtheenergyoftheelectrongasinseparateelementaryvolumesdvbyintegratingoverthewholevolumeoftheatom.Workinginthiswayandusingthecontinuityequation,Blokhintsevderivedanexpressionforthegasenergythat(inthestatisticalcase)coincidedwiththeexpressionobtainedearlierbyWeizsackerusingadifferentmethod.

Itisappropriatetonoteherethatthework”HydrodynamicsofanElectronGas”containsonemoreaspectthatdoesnotseemstrikingatfirstsightbutisnonethelessofgreatin-terest.Inessence,itwasshowninthisworkthatasysteminthelow-energylimitcanbecharacterizedbyasmallsetof”collective”(orhydrodynamic)variablesandequationsofmotioncorrespondingtothesevariables.Goingbeyondtheframeworkofthelow-energyregionwouldrequiretheconsiderationofplasmonexcitations,effectsofelectronshellrecon-structing,etc.Theexistenceoftwoscales,low-energyandhigh-energy,inthedescriptionofphysicalphenomenaisusedinphysics,explicitlyorimplicitly.Recently,thistopicobtainedinterestinganddeepdevelopment,connectedwiththeconceptofthe”quantum

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protectorate.”Inaworkwitharemarkabletitle,”TheTheoryofEverything”[14],authorsR.LaughlinandD.Pinesdiscussedthemostfundamentalprinciplesofthedescriptionofmatterinawidesense.Theauthorsputforwardthequestionwhatthe”TheoryofEverything”shouldbe.Intheiropinion,”itdescribestheeverydayworldofhumanbe-ings-air,water,rocks,fire,people,andsoforth”.Theanswergivenbytheauthorswasthat”thistheoryisnonrelativisticquantummechanics,”or,moreprecisely,theequationofnonrelativisticquantummechanics,whichtheywroteintheform

Hψ=−

h¯∂t.

(2)

Thatwastheonlyformulaintheirwork;theyalsogavedetaileddefinitionoftheHamil-tonianofasystemconsistingofmanyinteractingparticles.Theauthorsagreed,however,

that”Lessimmediatethingsintheuniverse,suchastheplanetJupiter,nuclearfission,thesun,orisotopicabundancesofelementsinspacearenotdescribedbythisequation,becauseimportantelementssuchasgravityandnuclearinteractionsaremissing.Butexceptforlight,whichiseasilyincluded,andpossiblygravity,thesemissingpartsareirrelevanttopeople-scalephenomena.Eq.(2)is,forallpracticalpurposes,theTheoryofEverythingforoureverydayworld.However,itisobviousglancingthroughthislistthattheTheoryofEv-erythingisnotevenremotelyatheoryofeverything.Weknowthisequation(2)iscorrectbecauseithasbeensolvedaccuratelyforsmallnumbersofparticles(isolatedatomsandsmallmolecules)andfoundtoagreeinminutedetailwithexperiment.However,itcannotbesolvedaccuratelywhenthenumberofparticlesexceedsabout10.Nocomputerexisting,orthatwilleverexist,canbreakthisbarrierbecauseitisacatastropheofdimension.IftheamountofcomputermemoryrequiredtorepresentthequantumwavefunctionofoneparticleisNthentheamountrequiredtorepresentthewavefunctionofkparticlesisNk.”AccordingtoR.LaughlinandD.Pines,”Theemergentphysicalphenomenaregulatedbyhigherorganizingprincipleshaveaproperty,namelytheirinsensitivitytomicroscopics,thatisdirectlyrelevanttothebroadquestionofwhatisknowableinthedeepestsenseoftheterm.Thelowenergyexcitationspectrumofaconventionalsuperconductor,forexample,iscompletelygenericandischaracterizedbyahandfulofparametersthatmaybedeterminedexperimentallybutcannot,ingeneral,becomputedfromfirstprinciples.Anevenmoretrivialexampleisthelow-energyexcitationspectrumofaconventionalcrystallineinsulator,whichconsistsoftransverseandlongitudinalsoundandnothingelse,regardlessofdetails.Itisratherobviousthatonedoesnotneedtoprovetheexistenceofsoundinasolid,foritfollowsfromtheexistenceofelasticmoduliatlonglengthscales,whichinturnfollowsfromthespontaneousbreakingoftranslationalandrotationalsymmetrycharacteristicofthecrystallinestate.Conversely,onethereforelearnslittleabouttheatomicstructureofacrystallinesolidbymeasuringitsacoustics.Thecrystallinestateisthesimplestknownexampleofaquantumprotectorate,astablestateofmatterwhosegenericlow-energyprop-ertiesaredeterminedbyahigherorganizingprincipleandnothingelse.Therearemanyofthese,theclassicprototypebeingtheLandaufermiliquid,thestateofmatterrepresentedbyconventionalmetalsandnormal3He...OtherimportantquantumprotectoratesincludesuperfluidityinBoseliquidssuchas4Heandthenewlydiscoveredatomiccondensates,superconductivity,bandinsulation,ferromagnetism,antiferromagnetism,andthequantumHallstates.Thelow-energyexcitedquantumstatesofthesesystemsareparticlesinexactlythesamesensethattheelectroninthevacuumofquantumelectrodynamicsisaparticle:

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Theycarrymomentum,energy,spin,andcharge,scatteroffoneanotheraccordingtosim-plerules,obeyFermiorBosestatisticsdependingontheirnature,andinsomecasesareeven”relativistic,”inthesenseofbeingdescribedquantitativelybyDiracorKlein-Gordonequationsatlowenergyscales.Yettheyarenotelementary,and,asinthecaseofsound,simplydonotexistoutsidethecontextofthestablestateofmatterinwhichtheylive.Thesequantumprotectorates,withtheirassociatedemergentbehavior,provideuswithexplicitdemonstrationsthattheunderlyingmicroscopictheorycaneasilyhavenomea-surableconsequenceswhatsoeveratlowenergies.Thenatureoftheunderlyingtheoryisunknowableuntiloneraisestheenergyscalesufficientlytoescapeprotection.”

Theexistenceoftwoscales,low-energyandthehigh-energy,inthedescriptionofmagneticphenomenawasstressedbyKuzemsky(seeRefs.[15,16,17])uponcomparativeinvesti-gationoflocalizedanditinerantquantummodelsofmagnetism.Theconceptofquantumprotectoratewasappliedtothetheoryofmagnetisminpaper[17].Wesucceededinfor-mulatingthecriterionofapplicabilityofquantummodelsofmagnetismtoparticularsub-stancesonthebasisofanalyzingtheirlow-energyandhigh-energyspectra.

In1940,Blokhintsev’sattentionwasattractedtotheproblemofstatisticaldescriptionofquantumsystems.Interesttotheseproblemsstemmedfromlecturesandworksonquan-tummechanicsbyL.I.MandelstamandK.V.Nikol’skii.Nikol’skii’sbookQuantumPro-cesses[18]ismentionedmanytimesinhispapers.Inthework”CorrelationofaQuantumEnsemblewithaClassicalGibbsEnsemble”(1940),thelimitingtransitionfromquantumequationsofmotionforthedensitymatrixtotheequationsofmotionfortheclassicaldistributionfunctionwasstudied.Blokhintsevstudiedthepossibilityofcorrespondencebetweentheclassicaldistributionfunctionf(q,p)andthequantumdensitymatrixρfromthegeneralpointofview.Forthispurpose,themixed(q,p)representationforthedensitymatrixwasused.Blokhintsevshowninthatpaperthattheredoesnotexistanydistri-butionfunctiondependingon(q,p)whichcoulddescribethequantumensemble.Inthenextworkonthetopic(1940),theproblemoftheconditionsofapproximationofquan-tumstatisticsbyclassicalstatisticswasconsidered.Itwasshownthatthereisnolimitingtransition(h→0)fromaquantumensembleconsistingofsimilarparticlestoaclassicalensemble.TheclassicaldescriptionisobtainedifthestateofthesystemischaracterizedbythepositioninthephasecellΩ≫h¯.Thus,intheseworks,anewdirectionofphysicswasinitiated:quantummechanicsinthephasespace[19].

ThetitleofthenextworkwrittenbyBlokhintsev(jointlywithYa.B.Dashevskiiin1941)is”PartitionofaSystemintoQuantumandClassicalParts.”Accordingtotheauthors,”Amongphysicalproblemsthatshouldbesolvedusingquantummechanicalmethods,therearesuchproblemsinwhichthesystemofinteractingparticlesunderstudyhasapropertythatoneofitspartsduringtheprocessesoccurringinthesystemmovesasthoughitobeysclassicallawsofmotion,i.e.,movingalongatrajectory.”Inthiswork,theystudiedthepossibilityofpartitioninganinteractingsystemintoquantumandclassicalparts.Theydemonstratedthetypeofperturbationwhentheclassicalpartactsonthequantumpart.Thisfieldattractedgreatinterestinsubsequentyears,especiallyinmanyproblemsofphysicalchemistry.Alargenumberofworksaredevotedtothistopic;someofthemareconsideredindetailinsurvey[20].

In1946,afterswitchingtodefenseproblems,Blokhintsevreturnedtoquantumphysics.Theworkperformedin1946istitled”CalculationoftheNaturalWidthofSpectralLinesUsingaStationaryMethod”.Thisshortworkdemonstratedhighflexibilityinhandling

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toolsofquantummechanicswhentheresultwasreachedinasimpleandelegantway.Blokhintsevwrote,”Usuallytheproblemofemissionandabsorptionoflightisconsideredusingthemethodofquantumtransitions.However,thisproblem,similartothedispersionproblem,canbesolvedinanextremelysimplewayusingthemethodofstationarystates”.Then,theauthorwroteoutthesystemofequationsforstateamplitudesoftwotypes:(a)whentheemitterisinthestatemandlightphotonsareabsent,and(b)whentheemitterisinthestatenandonelightphotonhasbeenemitted.Takingintoaccounttheenergyconservationlaw,thesolutionfortheamplitudewasobtained,andonitsbasis,theapproximateexpressionforthelevelpositionofthewholesystem(emitterandradiation).”ThisexpressionresultedinexactlythesameshiftandsmearingoflevelsasthoseobtainedbyDiracuponcalculationofresonancescattering.”Then,thespectraldistributionwithinthelinewidthwasfound.Theauthornotedthatupontransformationoftheamplitudetothecoordinaterepresentation,,”weobtainadivergentwavewithanamplitudethatslowlyincreaseswithincreasingdistancefromtheradiationsourceinthesamewayastookplaceforaclassicaldecayingoscillator”.

In1947,Blokhintsevpublishedthework”TheAtomunderanElectronMicroscope”.Blokhintsevwrotethat”thiswork,devotedtoaveryspecialproblem,isworthmention-ingduetoasomewhatunusualformulationoftheproblem.Theoriginisthus.Ipaidattentiontothefactthatundertheactionofascatteredelectron,theatomreceivesrecoilandcanbeknockedoutofitspositiononthesurfaceofthe’objectplate.’Ifitwerenotknockedoutatfirstscattering,itcouldbeknockedoutatsubsequentscattering.Itshouldbenotedthatthisexperimentisunusualfromthepointofviewofthecommonformulationofmeasurementsinaquantumensemble.Indeed,inthiscase,weconsidertherepetitionofmeasurementswiththesamesampleoftheatom,ratherthanasetofatoms,asisusuallydone.Aftereachmeasurementthestateoftheatom,generallyspeaking,changes,anditbecomesasampleofanotherquantumensemble.Thus,theseriesofscatteringnecessaryforobtaininganimageoftheatomconsistsofaseriesofscatteringrelatedtoobjectsfromdifferentquantumensembles.Thisseemstobeauniquecaseofsuchasituation.”

Sincephysicists,chemists,metallurgists,andbiologistsneededimprovedmicroscopes,thisproblemalwaysstirredinterest.ItshouldbenotedthatremarkableworkswereperformedbyMandelstamonthetheoryofthemicroscope.Mandelstamdisplayedhisinherentthestrengthanddepthofthoughtandhiskeenunderstandingofthephysicalnatureinan-alyzingthisproblem.Blokhintsev’sworkcontinuedthedevelopmentofthetheoryofthemicroscopeatthenewquantumstage.Theinterestinthisproblemnotonlystemmedfromtheappliedvalue.AccordingtoBlokhintsev,”Thedevelopmentofthetheoryofthemicroscopeisofinterestfromthetheoreticalpointofview,sincewhenobservingasin-gleatomusinganelectronmicroscope,theimagewillemergeasaresultofrepetitionofsinglescatteringactsonthesameobject,whileinquantummechanics,resultsareusuallyformulatedwithrespecttoasetofobjectsinthesameinitialstate.Duetotheactionontheatom,eachnewscatteringact,generallyspeaking,willforcetheatomtobeinanewinitialstate.Therefore,itisimportanttoanalyzetheinfluenceofelectronscatteringonthestateoftheobservedatom”.FurtherdevelopmentinphysicsprovedthatMandelstamandBlokhintsev’sinterestinproblemsofthetheoryofthemicroscopewasjustified.Thisdirectionwasdevelopedinsubsequentyearsgreatlyandisbeingextensivelydevelopednow.Blokhintsev’snameiscloselyrelatedtotheproblemofinterpretationofthequantummechanics[21].Blokhintsevrecollected[1]that”inthe1930s–1940s,theinterestof

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manyphysicists-theoreticiansattheLebedevPhysicsInstituteandMSUwasconcentratedontheprinciplesofquantummechanics,whichseemedfullofparadoxestomanypeople.”Alargenumberofhisbooks[22,23,24]andpapers[25,26]weredevotedtothisproblem.Hisviewsoftheproblemchangedandevolvedwithdeepeningandperfectionofarguments.Themosttopicalproblemsofinterpretingquantummechanicsweretheproblemofmea-surementandtheroleoftheobserver,andtheprobabilisticinterpretationofthewavefunction.Thevarietyofopinionsconcerningtheinterpretationofquantummechanicsin-creasedwithtime.Blokhintsevwrote[1]:”Thosediscussionsarereflectedinmyworks;thepolemicalcharacterofmypapersdevotedtocriticalanalysisoftheideasoftheCopen-hagenschoolandthoseofFockgraduallybroughtmetoaconsistentmaterialisticconceptofquantumensemblesandmathematicalmeasurementtheory.Onlyinthe1960s,afterdiscussionswiththeHungarianphysicistL.Janosi,didImanagetoformulateareasonabletheoryofquantummeasurementsfreefrominconsistenciesininterpretingtheroleoftheob-server.Inthisnewconcept,themeasuringdeviceanditsinteractionwiththemicroobjectweretransformedfromthesubjectofphilosophicaldiscussionstothesubjectoftheoreticalphysics”.

Asaresultoflongtermresearchandreflections,Blokhintsevdevelopedhisownap-proachtointerpretingquantummechanics,whichincludedideasputforwardbyJ.vonNeumann,L.I.Mandelstam,andK.V.Nikol’skii.Itwascalledtheinterpretationofquan-tummechanicsonthebasisofquantumensembles.Hewroteinasummarywork[24],”ThepresentationofquantummechanicsundertakenintheselecturesisessentiallybasedontheideasofvonNeumann,whichintheirtimeattractedtheattentionoftheMoscowschooloftheoreticians;in1930sthisschoolwasheadedbyAcademicianMandelstam;alsoNikol’skiicontributedconsiderablytoourunderstandingofquantummechanics.”Blokhint-sevthoughtthat”thisapproachtotheprinciplesofquantummechanicshadanadvantage,ascomparedtotraditionalinterpretationsonthebasisofthewavefunction,sinceitallowedonetoincludethetheoryofquantummeasurementsasachapterofquantummechanics”.InBlokhintsev’sapproach,thestatisticaloperatordescribingthestateofthemicrosysteminaquantumensembleofthegeneraltypeplaystheprimaryrole.Thewavefunctiondescribesaspecialtypeofquantumensemble,thecoherentensemble.Blokhintsev’sap-proachtotheinterpretationofquantummechanicsbecamewidelyknown.DeWittandGraham[27]intheirsurveyofdifferentapproachestointerpretingquantummechanicswroteaboutBlokhintsev’sbooks:”...theyarebothverywellwrittenandinformative.Thedeparturefromorthodoxyoccurs,infact,onlyincertainattitudesandchoiceofwords,whilethegeneralpresentationofquantummechanicsisrefreshing...;[thesecondbook]con-tainsanexcellentaccountofmeasurementtheory”.Blokhintsev’sapproachtointerpretingquantummechanicsisaconstituentpartofthescopeofideasofvariousresearchers.Oneoftheauthoritativehistoriansofquantummechanics,Hooker[28],notedthat”...Einsteinandhisco-workersPodolskyandRosen,Blokhintsev,Bopp,deBroglie,Popper,Schrodinger,Lande,andmostrecentlyBallentineconstituteasmallgroupofphysicistsandphilosophers,whoaredeterminedtotreatquantumtheoryasaspeciesofstatisticalmechanics,manyofthemhopingultimatelytoreinstatetheclassicalconceptionofreality.”Adetailedsurveyoftheinterpretationofquantummechanicsonthebasisofquantumensemblescanbefoundin[29].Theinterpretationofquantummechanicsonthebasisofquantumensemblesisoneofmanyinexistence.Thus,theinterpretationofquantummechanicsonthebasisofquantumensemblesoccupiesaseparate(noticeable)placeamongotherpossibleapproaches

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tointerpretationofquantummechanics.InterpretationofquantummechanicsonthebasisofquantumensembleswasconsideredindetailbyYa.A.Smorodinskii(1986).Theconclu-sionhemadeisquiteremarkable[30]:”Discussionshowedthatifthetheoryofquantumensemblesisused,theseensemblesshouldbeassignedunusualpropertiesthatcouldnotbeconsistentwithcommonprobabilitytheory;thesepropertiesarenotmanifestedforoneparticleandcanbefoundonlyincorrelatedeffects;similartonon-Euclideangeometrynecessaryforthedescriptionofthevelocityspaceinspecialrelativity,quantummechanicshasgeneratedthenon-Kolmogorovprobabilitytheory;thisisprobablythedeepmeaningofanalysisofthepropertiesofaquantumensemble”(seealsorecentbook[31]).

WeconcludethispaperwiththewordsbyMaxBornformulatedinhislecture”Exper-imentandTheoryinPhysics”deliveredin1943.”Thosewhowanttomastertheartofscientificpredictionshould,insteadofrelyingonabstractdeduction,trytocomprehendthesecretlanguageofNature,whichisrepresentedbyexperimentaldata.”Blokhintsevinhislecturesandtalksmorethanonceexpressedsimilarthoughts,maybeinslightlydifferentwords.Inthesenotesandintheextendedreview[3]wehavetriednotonlytowriteaboutBlokhintsev’sstudies,butbuildthemintoappropriatelinesofthedevelopmentofquan-tumphysicsandconnectthem,directlyorindirectly,tothemoderndevelopmentofthesefieldsofscience.WehavetriedtoshowthatBlokhintsev’sbookQuantumMechanics[22],whichisjustlyconsideredoneofthebesttextbooksinquantumphysics,wascompiledbyawitnesstoandaparticipantintheformationanddevelopmentofquantummechanics.Itorganicallyincludesmostofhisoriginalworksinanintegrateddescriptionofthesubject.This,togetherwiththedefiniteliterarytalentoftheauthorandhisgiftforpresentingthesubjectclearlyandlucidly,isthebackgroundonwhichthebookQuantumMechanicsstands,anditcontinuestodescribestheworldusingthelanguageofaquantum!

Inthisworkduetothelackofspace,notallthetopicsandproblemsthatIwantedtodiscussarehere.PermitmetoreferanyreaderwhowantstoreflectonBlokhintsev’sworkstoacollectionofselectedworksintwovolumesthatwillbepublishedin2008inMoscow.Amoredetaileddiscussionofmodernapproachestointerpretingquantummechanicscanbefoundinpaper[3].ThefulldetailsandpreciseReferencesaregiveninpaper[3]aswell.

References

[1]D.I.Blokhintsev,MyWayintheScience(Self-ReviewofWorks),B.M.Barbashovand

A.N.SissakianEds.,Dubna,JINRPublishing,2007.[2]V.Rich,Nature278,765(1979).

[3]A.L.Kuzemsky,FizikaElementarnichChasticiAtomnogoJadra39,5(2008);

PhysicsofParticlesandNuclei,39,137(2008).

[4]M.Jammer,ConceptualDevelopmentofQuantumMechanics,NewYork,McGraw-Hill,1966.

[5]R.W.Gurney,ElementaryQuantumMechanics,Cambridge,CambridgeUniversity

Press,1934.

[6]N.F.Mott,H.Jones,TheTheoryofthePropertiesofMetalsandAlloys.Oxford,

ClarendonPress,1936.

[7]S.I.Pekar,InvestigationsonElectronicTheoryofCrystalsMoscow,GTTI,1951.[in

Russian].

11

[8]Ya.A.Smorodinskii,Usp.Fiz.Nauk39,325(1949).

[9]In:Proc.ofScienceSeminarof85yearofD.I.Blokhintsev,Dubna,27Jan.,1993,25

Jan.,1994,Dubna,JINRPublishing,1995.

[10]G.L.Trigg,LandmarkExperimentsinTwentiethCenturyPhysics,NewYork,Crane,

RussakandCo.,1975.

[11]P.Beiersdorfer,H.Chen,D.B.Thom,andE.Trabert,Phys.Rev.Lett.95,233003

(2005).

[12]V.Weisskopf,PhysicsintheTwentiethCentury,Cambridge,MITPress,1972.

[13]J.MehraandK.A.Milton,ClimbingtheMountain.TheScientificBiographyofJulian

Schwinger,Oxford,OxfordUniversityPress,2000.

[14]R.D.Laughlin,D.Pines,Proc.Natl.Acad.Sci.USA.97,28(2000).

[15]A.L.Kuzemsky,FizikaElementarnichChasticiAtomnogoJadra12,366(1981)[in

Russian];Sov.J.Part.Nucl.12,146(1981).

[16]A.L.Kuzemsky,FundamentalPrinciplesofthePhysicsofMagnetismandtheProblem

ofItinerantandLocalizedElectronicStates.JINRCommun.E17-2000-32.Dubna,2000.22p.

[17]A.L.Kuzemsky,Intern.J.Mod.Phys.,B12,803(2002);(cond-mat/0208222).[18]K.V.Nikolskii,QuantumProcesses,Moscow,GTTI,1940[inRussian].

[19]C.Zachos,D.Fairlie,T.Curtright,QuantumMechanicsinPhaseSpace,Singapore,

WorldScientific,2005.

[20]R.Kapral,ProgressintheTheoryofMixedQuantum-ClassicalDynamics.

Annu.Rev.Phys.Chem.57,129(2006).

[21]M.Jammer,PhilosophyofQuantumMechanics,NewYork,JohnWileyandSons,

1974.

[22]D.I.Blokhintsev,QuantumMechanics,GordonandBreachPublishing,NewYork,

19.

[23]D.I.Blokhintsev,PhilosophyofQuantumMechanics,Dordrecht,D.ReidelPublishing,

1968.

[24]D.I.Blokhintsev,QuantumMechanics.LecturesonSelectedQuestions,Atomizdat,

Moscow,1981.[inRussian]

[25]D.I.Blokhintsev,Usp.Fiz.Nauk,95,75(1968)[Phys.-Usp.11,320(1968)].[26]D.I.Blokhintsev,Usp.Fiz.Nauk,122,745(1977)[Phys.-Usp.20,683(1977)][27]B.S.DeWitt,R.N.Graham,Am.J.Phys.39,724(1971).

[28]C.A.Hooker,TheNatureofQuantumMechanicalReality:EinsteinversusBohr,in:

ThePittsburghStudiesinthePhilosophyofScience.Pittsburgh:PittsburghUP,1972.Vol.5,P.67.

[29]D.Home,M.A.B.Whitaker,Phys.Rep.210,223(1992).

[30]Ya.A.Smorodinskii,”OntheQuantumEnsembles,”in:Proc.ofScienceSeminarDe-votedto75YearfromBirthdayofD.I.Blokhintsev,Dubna,23Jan.,1983(Dubna,JINR,1986),pp.92-97.

[31]A.Yu.Khrennikov,Non-Kolmogorov’sProbabilityTheoriesandQuantumPhysics,

Moscow,Fizmatlit,2003[inRussian].

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