Physical Kinetics: Classical and Quantum Problems and Solutions

245 Pages·2022·1.891 MB·English

by  Serguei N. Burmistrov

Serguei N. Burmistrov
Physical
Kinetics
Classical and Quantum Problems
and Solutions
Physical Kinetics
Serguei N. Burmistrov
Physical Kinetics
Classical and Quantum Problems
and Solutions
SergueiN.Burmistrov
KurchatovInstitute
Moscow,Russia
ISBN 978-981-19-1648-9 ISBN 978-981-19-1649-6 (eBook)
https://doi.org/10.1007/978-981-19-1649-6
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Forstudentsstudyingthephysicalkinetics
Preface to the English Edition
The Russian edition of this book came to light 5 years ago. The present edition
is augmented with new problems, increasing their number from 40 to 60. All the
novel problems refer to new sections of physical kinetics. They are the following:
the Lindblad master equation, ballistic transport in quantum microcontacts, weak
localization effects, kinetics of first-order phase transitions (the Stefan problem),
kineticphenomenaatthesuperfluid-solidhelium,andrarefiedBoseandFermigases.
ThemisprintsrevealedintheRussianeditionarecorrectedaswell.
Using this opportunity, the author would like to express his gratitude to all
colleaguesattheDepartmentofTheoreticalPhysicsinMoscowInstituteofPhysics
andTechnology.Inaddition,IamalsogratefultoProf.N.M.Shchelkachevforthe
fruitfuldiscussionofquestionsconcerningtheselectionofproblemsforthepractical
classesonthephysicalkineticsattheMIPTGeneralandAppliedPhysicsFaculty.
Moscow,Russia SergueiN.Burmistrov
January2021
vii
Preface
Tostudyphysicalkineticsand,mostimportantly,tomasteritsmethodsofstudying
thethermodynamicallynon-equilibriumsystems,itisnotsufficienttoberestricted
withlisteningtothelecturecourseandconsideringthetheoreticalassertions.Thus,
the physical kinetics course includes the practical classes aimed at facilitating the
studentstomasterinsolvingtheproblems.Solvingtheproblemsgivesthestudents
an opportunity to test their real knowledge which, in ideal, should not be a set of
memorizedinformationalone.Fortheteacher,everyproblemsolvedindependently
by the student is the most effective indicator of comprehending the subject. The
problemself-solvingdevelopsandeducatestheanalyticalandcreativethinking.
Itismuchmoredifficulttomasterthephysicalkineticsandlearnhowtoapply
itsmethodsinpracticecomparedastomasterinsuchfieldsoftheoreticalphysicsas
statisticalphysics,quantummechanics,orfieldtheory.Thefactisthatthephysical
kineticsconsistsofmanycompletelyversatilefields,forexample,kinetictheoryof
gases, plasma theory, transport phenomena in metals, semiconductors, dielectrics,
anddisorderedmedia,kineticphenomenainquantumcrystalsandliquids,andphase
transition kinetics. In general, in order to describe the kinetic phenomena in each
such field of physics, we have to use and apply specific models and methods. As
a rule, the models and methods are very complicated and require the cumbersome
calculationswhichcansimplybeunattainablewithoutspecialmathematicaltraining.
Ontheotherhand,thestudyofphysicalkineticsundoubtedlyrequiresthemastering
of practical methods for solving various problems. Solving the specific tasks is a
perfectadditiontothelecturecourse.Theanalysisofthesolutionhelpsthestudent
tounderstandbetterthelecturecourseasawhole.
Thebookisbasedonthepracticalclassesforthestudentsstudyingthephysical
kinetics in the general course of theoretical physics at the General and Applied
PhysicsFacultyofMoscowInstituteofPhysicsandTechnology.Theproblemshave
beenincludedinthestudents’homeworks.Inordertopresentthebasicsofphysical
kineticsinaformaccessibletophysicsstudentswhodonotnecessarilyspecializeas
futuretheoreticalphysicists,wetriedtoavoidusingcomplexdiagrammatic,renorm-
group, and other special mathematical tools of theoretical physics. As a rule, the
presentation of the material is based on simple representations of the Boltzmann
ix
x Preface
transportequationorLindbladmasterequation.Alltheproblemsaresuppliedwith
thedetailedsolutionsandcommentsexplainingthemotivationoftheproblemsand
their connection with various problems of modern physical kinetics. The section
withtheproblemconditionsisprecededbythebriefintroductionthatcontainsthe
necessaryinformationandnotionsusefulforsolvingandunderstandingtheproblems
proposed.
Thebookcanbeusedasasupplementtothetextbookspublishedonthephysical
kinetics.Thepurposeofthebookistohelpstudentsintrainingthepracticalskillsand
masteringthebasicelementsofphysicalkinetics.Tounderstandthesubjectmatter,
itissufficienttoknowthetraditionalcoursesoftheoreticalphysicsatthephysical
universities.Thephysicaluniversalityofthepresentationaswellastheanalysisof
alargenumberofspecificphysicalproblemsallowsthisbooktoserveasatextbook
forallstudentsstudyingthephysicalkinetics.
In conclusion, the author expresses his sincere gratitude to the entire team of
teachersattheTheoreticalPhysicsDepartmentofMoscowInstituteofPhysicsand
Technology.
Moscow,Russia SergueiN.Burmistrov
About This Book
Thebookcontains60problemsofvariousdegreesofcomplexity.Theproblemsare
based on the materials for the practical classes in the course of physical kinetics
with the students of General and Applied Physics Faculty at Moscow Institute of
PhysicsandTechnology.Alltheproblemsareprovidedwiththedetailedsolutions.
Thecommentstotheproblemsreflecttheconnectionwiththeproblemsandmethods
ofmodernphysicalkinetics.Abriefintroductiongivesthenecessaryinformationfor
solvingandunderstandingtheproblems.
The book is proposed for students and postgraduates studying the theoretical
physics.
xi
Contents
1 BriefReminders ............................................... 1
1.1 TheBoltzmannTransportEquation .......................... 1
1.2 TheGeneralizedSusceptibilityandtheLinearResponse ........ 4
1.3 TheFluctuation-DissipationTheorem ........................ 6
1.4 TheOnsagerReciprocalRelations ........................... 7
1.5 TheLindbladMasterEquation .............................. 10
2 Problems ...................................................... 13
2.1 TheLangevinEquationandtheFluctuation-Dissipation
Theorem ................................................. 13
2.2 TheBoltzmannTransportEquationintheτ-Approximation:
TheThermoelectricEffectsinConductors .................... 13
2.3 GalvanomagneticEffectsinMetals .......................... 15
2.4 KineticPhenomenainaMetalandNormalFermiLiquid ........ 15
2.5 Electron-Phonon Scattering in a Metal: The Transport
Coefficients .............................................. 16
2.6 TheElectronScatteringwithMagneticImpurities:The
KondoEffect ............................................. 18
2.7 WeakLocalizationEffectsinaMetalwithImpurities ........... 19
2.8 BallisticElectronTransportintheMesoscopicSystems ......... 21
2.9 TheRarifiedBoseandFermiGases .......................... 22
2.10 TheHoppingMottConductivityandtheCoulombGap ......... 23
2.11 KineticsofPhononsandThermalConductivityinDielectrics .... 24
2.12 TheHydrodynamicsofNormalandSuperfluidLiquids:
SoundOscillationsandEnergyDissipation .................... 24
2.13 Kapitza Resistance and Kinetic Phenomena
attheSuperfluid-SolidHeliumInterface ...................... 25
2.14 CollisionlessPlasma:ThePermittivityandtheLongitudinal
andTransverseOscillations ................................. 28
2.15 Kinetics of First-Order Phase Transitions: Melting
andSolidification .......................................... 28
xiii