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Kinetic Theory: Classical, Quantum, and Relativistic Descriptions, Third Edition Richard L. Liboff Springer Graduate Texts in Contemporary Physics Series Editors: R. Stephen Berry Joseph L. Birman Mark P. Silverman H. Eugene Stanley Mikhail Voloshin Springer NewYork Berlin Heidelberg HongKong London Milan Paris Tokyo This page intentionally left blank Richard L. Liboff Kinetic Theory Classical, Quantum, and Relativistic Descriptions Third Edition With112Illustrations 1 3 RichardL.Liboff SchoolofElectricalEngineering CornellUniversity Ithaca,NY14853 [email protected] SeriesEditors R.StephenBerry JosephL.Birman MarkP.Silverman DepartmentofChemistry DepartmentofPhysics DepartmentofPhysics UniversityofChicago CityCollegeofCUNY TrinityCollege Chicago,IL60637 NewYork,NY10031 Hartford,CT06106 USA USA USA H.EugeneStanley MikhailVoloshin CenterForPolymerStudies TheoreticalPhysicsInstitute PhysicsDepartment TateLaboratoryofPhysics424 BostonUniversity TheUniversityofMinnesota Boston,MA02215 Minneapolis,MN55455 USA USA LibraryofCongressCataloging-in-PublicationData Liboff,RichardL.,1931– Kinetictheory:classical,quantum,andrelativisticdescriptions/RichardL.Liboff 3rded. p.cm.—(Graduatetextsincontemporaryphysics) Includesbibliographicalreferencesandindex. ISBN0-387-95551-8(alk.paper) 1.Kinetictheoryofmatter. I.Title. II.Series. QC174.9L542003 530.13(cid:1)6—dc21 2002026658 ISBN0-387-95551-8 Printedonacid-freepaper. Thesecondeditionofthisbookwaspublished©1998byJohnWiley&Sons. ©2003Springer-VerlagNewYork,Inc. Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permissionofthepublisher(Springer-VerlagNewYork,Inc.,175FifthAvenue,NewYork,NY10010, USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnection withanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orby similarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,evenifthey arenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyare subjecttoproprietaryrights. PrintedintheUnitedStatesofAmerica. 9 8 7 6 5 4 3 2 1 SPIN10887268 www.springer-ny.com Springer-Verlag NewYork Berlin Heidelberg AmemberofBertelsmannSpringerScience+BusinessMediaGmbH TotheMemoryof HaroldGrad TeacherandFriend This page intentionally left blank I learned much from my teachers, more frommycolleaguesandmostofallfrom mystudents RabbiJudahha-Nasi(ca.135–C.E.) BabylonianTalmud(Makkot,10a) LudwigBoltzmann(UniversityofVienna,courtesyAIPEmilioSegre` Visual Archives) Preface to the Third Edition Sincethefirsteditionofthiswork,kinetictheoryhasmaintaineditspositionas acornerstoneofanumberofdisciplinesinscienceandmathematics.Inphysics, such is the case for quantum and relativistic kinetic theory. Quantum kinetic theory finds application in the transport of particles and radiation through material media, as well as the non-stationary quantum–many-body problem. Relativistickinetictheoryisrelevanttocontrolledthermonuclearfusionandto anumberofproblemsinastrophysics.Inappliedmathematics,kinetictheory relatestothephenomenaoflocalization,percolation,andhopping,relevantto transportpropertiesinporousmedia.Classicalkinetictheoryisthefoundation offluiddynamicsandthusisimportanttoaerospace,mechanical,andchemical engineering. Important to the study of transport in metals is the Lorentz– Legendreexpansion,whichinthisneweditionappearsinanappendix.Anew sectioninChapter1wasincludedinthisneweditionthataddressesconstantsof motionandsymmetry.Anumberofsmallbutimportantrevisionswerelikewise madeinthisnewedition.Amorecompletedescriptionofthecontentsofthe textfollows. Thetextcomprisessevenchapters.InChapter1,thetransformationtheory ofclassicalmechanicsisdevelopedforthepurposeofderivingLiouville’sthe- orem and the Liouville equation. Four distinct interpretations of the solution tothisequationarepresented.ThefourthinterpretationaddressesGibbs’sno- tionofadistributionfunctionthatistheconnectinglinkbetweentheLiouville equation and experimental observation. The notion of a Markov process is discussed,andthecentral-limittheoremisderivedandappliedtotherandom walkproblem. In Chapter 2, the very significant BBKGY hierarchy is obtained from the Liouvilleequation,andthefirsttwoequationsofthissequenceareappliedin the derivation of conservation of energy for a gas of interacting particles. In