电子液体量子理论

电子液体量子理论

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作者: 朱利安尼著

出版社: 世界图书出版公司

出版时间: 2011-01

版次: 1

ISBN: 9787510029646

定价: 129.00

装帧: 平装

开本: 16开

纸张: 胶版纸

页数: 777页

分类: 自然科学

39人买过

Theelectronliquidparadigmisatthebasisofmostofourcurrentunderstandingofthephysicalpropertiesofelectronicsystems.Quiteremarkably,thelatterarenowadaysattheintersectionofthemostexcitingareasofscience：materialsscience,quantumchem-istry,nano-electronics,biology,andquantumcomputation.Accordingly,itsimportancecanhardlybeoverestimated.Thefieldisparticularlyattractivenotonlyforthesimplicityofitsclassicformulation,butalsobecause,byitsverynature,itisstillpossibleforindividualresearchers,armedwiththoughtfulnessanddedication,andsurroundedbyasmallgroupofcollaborators,tomakedeepcontributions,inthebesttraditionof"smallscience". preface
1introductiontotheelectronliquid
1.1ataleofmanyelectrons
1.2wheretheelectronsroam：physicalrealizationsoftheelectronliquid
1.2.1threedimensions
1.2.2twodimensions
1.2.3onedimension
1.3themodelhamiitonian
1.3.1jeiliummodel
1.3.2coulombinteractionregularization
1.3.3theelectronicdensityasthefundamentalparameter
1.4secondquantization
1.4.1fockspaceandtheoccupationnumberrepresentation
1.4.2representationofobservables
1.4.3constructionofthesecond-quantizedhamiltonian
1.5theweakcouplingregime
1.5.1thenoninteractingelectrongas
1.5.2noninteractingspinpolarizedstates
1.5.3theexchangeenergy
1.5.4exchangeenergyinspinpolarizedstates
1.5.5exchangeandthepaircorrelationfunction
1.5.6all-ordersperturbationtheory：therpa
1.6thewignercrystal
1.6.1classicalelectrostaticenergy
1.6.2zero-pointmotion
1.7phasediagramoftheelectronliquid
1.7.1thequantummontecarloapproach
1.7.2theground-stateenergy
1.7.3experimentalobservationoftheelectrongasphases
1.7.4exoticphasesoftheelectronliquid
1.8equilibriumpropertiesoftheelectronliquid
1.8.1pressure，compressibility，andspinsusceptibility
1.8.2thevirialtheorem
1.8.3theground-stateenergytheorem
exercises

2thehartree——fockapproximation
2.1introduction
2.2formulationofthehartree-focktheory
2.2.1thehartree-fockeffectivehamiltonian
2.2.2thehartree-fockequations
2.2.3ground-stateandexcitationenergies
2.2.4twostabilitytheoremsandthecoulombgap
2.3hartree-fockfactorizationandmeanfieldtheory
2.4applicationtotheuniformelectrongas
2.4.1theexchangeenergy
2.4.2polarizedversusunpolarizedstates
2.4.3compressibilityandspinsusceptibility
2.5stabilityofhartree——fockstates
2.5.1basicdefinitions：localversusglobalstability
2.5.2localstabilitytheory
2.5.3localandglobalstabilityforauniformlypolarizedelectrongas
2.6spindensitywaveandchargedensitywavehartree-fockstates
2.6.1hartree-focktheoryofspiralspindensitywaves
2.6.2spindensitywaveinstabilitywithcontactinteractionsinonedimension
2.6.3proofofoverhauser'sinstabilitytheorem
2.7bcsnonnumber-conservingmeanfieldtheory
2.8localapproximationstotheexchange
2.8.1slater'slocalexchangepotential
2.8.2theoptimizedeffectivepotential
2.9real-worldhartree-focksystems
exercises

3linearresponsetheory
3.1introduction
3.2generaltheoryoflinearresponse
3.2.1responsefunctions
3.2.2periodicperturbations
3.2.3exacteigenstatesandspectralrepresentations
3.2.4symmetryandreciprocityrelations
3.2.5originofdissipation
3.2.6time-dependentcorrelationsandthefiuctuation——dissipationtheorem
3.2.7analyticpropertiesandcollectivemodes
3.2.8sumrules.
3.2.9thestiffnesstheorem
3.2.10bogoliubovinequality
3.2.11adiabaticversusisothermalresponse
3.3densityresponse
3.3.1thedensity——densityresponsefunction
3.3.2thedensitystructurefactor
3.3.3high-frequencybehaviorandsumrules
3.3.4thecompressibilitysumrule
3.3.5totalenergyanddensityresponse
3.4currentresponse
3.4.1thecurrent——currentresponsefunction
3.4.2gaugeinvariance
3.4.3theorbitalmagneticsusceptibility
3.4.4electricalconductivity：conductorsversusinsulators
3.4.5thethirdmomentsumrule
3.5spinresponse
3.5.1densityandlongitudinalspinresponse
3.5.2high-frequencyexpansion
3.5.3transversespinresponse
exercises

4linearresponseofindependentelectrons
4.1introduction
4.2linearresponseformalismfornon-interactingelectrons
4.3densityandspinresponsefunctions
4.4thelindhardfunction
4.4.1thestaticlimit
4.4.2theelectron-holecontinuum
4.4.3thenatureofthesingularityatsmallqandto
4.4.4thelindhardfunctionatfinitetemperature
4.5transversecurrentresponseandlandaudiamagnetism
4.6elementarytheoryofimpurityeffects
4.6.1derivationofthedrudeconductivity
4.6.2thedensity-densityresponsefunctioninthepresenceofimpurities
4.6.3thediffusionpole
4.7meanfieldtheoryoflinearresponse
exercises

5linearresponseofaninteractingelectronliquid
5.1introductionandguidetothechapter
5.2screenedpotentialanddielectricfunction
5.2.1thescalardielectricfunction
5.2.2properversusfulldensityresponseandthecompressibilitysumrule
5.2.3compressibilityfromcapacitance
5.3therandomphaseapproximation
5.3，1therpaastime-dependenthartreetheory
5.3.2staticscreening
5.3.3plasmons
5.3.4theelectron-holecontinuuminrpa
5.3.5thestaticstructurefactorandthepaircorrelationfunction
5.3.6therpaground-stateenergy
5.3.7critiqueoftherpa
5.4themany-bodylocalfieldfactors
5.4.1localfieldfactorsandresponsefunctions
5.4.2many-bodyenhancementofthecompressibilityandthespinsusceptibility
5.4.3staticresponseandfriedeloscillations
5.4.4thestlsscheme
5.4.5multicomponentandspin-polarizedsystems
5.4.6currentandtransversespinresponse
5.5effectiveinteractionsintheelectronliquid
5.5.1testcharge——testchargeinteraction
5.5.2electron-testchargeinteraction
5.5.3electron-electroninteraction
5.6exactpropertiesofthemany-bodylocalfieldfactors
5.6.1wavevectordependence
5.6.2frequencydependence
5.7theoriesofthedynamicallocalfieldfactor
5.7.1thetime-dependenthartree-fockapproximation
5.7.2firstorderperturbationtheoryandbeyond
5.7.3themode-decouplingapproximation
5.8calculationofobservableproperties
5.8.1plasmondispersionanddamping
5.8.2dynamicalstructurefactor
5.9generalizedelasticitytheory
5.9.1elasticityandhydrodynamics
5.9.2visco-elasticconstantsoftheelectronliquid
5.9.3spindiffusion
exercises

6theperturbativecalculationoflinearresponsefunctions
6.1introduction
6.2zero-temperatureformalism
6.2.1time-orderedcorrelationfunction
6.2.2theadiabaticconnection
6.2.3thenon-interactinggreen'sfunction
6.2.4diagrammaticperturbationtheory
6.2.5fouriertransformation
6.2.6translationa！iyinvariantsystems
6.2.7diagrammaticcalculationofthelindhardfunction
6.2.8first-ordercorrectiontothedensity-densityresponsefunction
6.3integralequationsindiagrammaticperturbationtheory
6.3.1properresponsefunctionandscreenedinteraction
6.3.2green'sfunctionandself-energy
6.3.3skeletondiagrams
6.3.4irreducibleinteractions
6.3.5self-consistentequations
6.3.6two-bodyeffectiveinteraction：thelocalapproximation
6.3..7extensiontobrokensymmetrystates
6.4perturbationtheoryatfinitetemperature
exercises

7densityfunctionaltheory
7.1introduction
7.2ground-stateformalism
7.2.1thevariationalprincipleforthedensity
7.2.2thehohenberg-kohntheorem
7.2.3thekohn——shamequation
7.2.4meaningofthekohn-shameigenvalues
7.2.5theexchange-correlationenergyfunctional
7.2.6exactpropertiesofenergyfunctionals
7.2.7systemswithvariableparticlenumber
7.2.8derivativediscontinuitiesandthebandgapproblem
7.2.9generalizeddensityfunctionaltheories
7.3approximatefunctionais
7.3.1thethomas-fermiapproximation
7.3.2thelocaldensityapproximationfortheexchange-correlationpotential
7.3.3thegradientexpansion
7.3.4generalizedgradientapproximation
7.3.5vanderwaalsfunctionals
7.4currentdensityfunctionaltheory
7.4.1thevorticityvariable
7.4.2thekohn-shamequation
7.4.3magneticscreening
7.4.4thelocaldensityapproximation
7.5time-dependentdensityfunctionaltheory
7.5.1therunge——grosstheorem
7.5.2thetime-dependentkohn-shamequation
7.5.3adiabaticapproximation
7.5.4frequency-dependentlinearresponse
7.6thecalculationofexcitationenergies
7.6.1finitesystems
7.6.2infinitesystems
7.7reasonforthesuccessoftheadiabaticlda
7.8beyondtheadiabaticapproximation
7.8.1thezero-forcetheorem
7.8.2the"ultra-nonlocality"problem
7.9currentdensityfunctionaltheoryandgeneralizedhydrodynamics
7.9.1thexcvectorpotentialinahomogeneouselectronliquid
7.9.2theexchange-correlationfieldintheinhomogeneouselectronliquid
7.9.3thepolarizabilityofinsulators
7.9.4spincurrentdensityfunctionaltheory
7.9.5linewidthofcollectiveexcitations
7.9.6nonlinearextensions
exercises

8thenormalfermiliquid
8.1introductionandoverviewofthechapter
8.2thelandaufermiliquid
8.3macroscopictheoryoffermiliquids
8.3.1thelandauenergyfunctional
8.3.2theheatcapacity
8.3.3thelandaufermiliquidparameters
8.3.4thecompressibility
8.3.5theparamagneticspinresponse
8.3.6theeffectivemass
8.3.7theeffectsoftheelectron-phononcoupling
8.3.8measuringm*，k，g*andxs
8.3.9thekineticequation
8.3.10theshearmodulus
8.4simpletheoryofthequasiparticlelifetime
8.4.1generalformulas
8.4.2three-dimensionalelectrongas
8.4.3two-dimensionalelectrongas
8.4.4exchangeprocesses
8.5microscopicunderpinningofthelandautheory
8.5.1thespectralfunction
8.5.2themomentumoccupationnumber
8.5.3quasiparticleenergy，renormalizationconstant，andeffectivemass
8.5.4luttinger'stheorem
8.5.5thelandauenergyfunctional
8.6therenormalizedhamiitonianapproach
8.6.1separationofslowandfastdegreesoffreedom
8.6.2eliminationofthefastdegreesoffreedom
8.6.3thequasiparticlehamiltonian
8.6.4thequasiparticleenergy
8.6.5physicalsignificanceoftherenormalizedhamiltonian
8.7approximatecalculationsoftheself-energy
8.7.1thegwapproximation
8.7.2diagrammaticderivationofthegeneralizedgwseif-energy
8.8calculationofquasiparticleproperties
8.9superconductivitywithoutphonons?
8.10thedisorderedelectronliquid
8.10.1thequasiparticlelifetime
8.10.2thedensityofstates
8.10，3coulomblifetimesandweaklocalizationintwo-dimensionalmetals
exercises

9electronsinonedimensionandtheluttingerliquid
9.1non-fermiliquidbehavior
9.2theluttingermodel
9.3theanomalouscommutator
9.4introducingthebosons
9.5solutionoftheluttingermodel
9.5.1exactdiagonalization
9.5.2physicalproperties
9.6bosonizationofthefermions
9.6.1constructionofthefermionfields
9.6.2commutationrelations
9.6.3constructionofobservables
9.7thegreen'sfunction
9.7.1analyticalformulation
9.7.2evaluationoftheaverages
9.7.3non-interactinggreen'sfunction
9.7.4asymptoticbehavior
9.8thespectralfunction
9.9themomentumoccupationnumber
9.10densityresponsetoashort-rangeimpurity
9.1！theconductanceofaluttingerliquid
9.12spin-chargeseparation
9.13long-rangeinteractions
exercises

10thetwo-dimensionalelectronliquidathighmagneticfield
10.1introductionandoverview
10.2one-electronstatesinamagneticfield
10.2.1energyspectrum
10.2.2one-electronwavefunctions
10.2.3fock-darwinlevels
10.2.4lowestlandaulevel
10.2.5coherentstates
10.2.6effectofanelectricfield
10.2.7slowlyvaryingpotentialsandedgestates
10.3theintegralquantumhalleffect
10.3.1phenomenology
10.3.2the"edgestate"approach
10.3.3stredaformula
10.3.4thelaughlinargument
10.4electronsinfulllandaulevels：energetics
10.4.1noninteractingkineticenergy
10.4.2densitymatrix
10.4.3paircorrelationfunction
10.4.4exchangeenergy
10.4.5the"lindhard"function
10.4.6staticscreening
10.4.7correlationenergy-therandomphaseapproximation
10.4.8fractionalfillingfactors
10.5exchange-driventransitionsintiltedfield
10.6electronsinfulllandaulevels：dynamics
10.6.1classificationofneutralexcitations
10.6.2collectivemodes
10.6.3time-dependenthartree-focktheory
10.6.4kohn'stheorem
10.7electronsinthelowestlandaulevel
10.7.1onefulllandaulevel
10.7.2two-particlestates：haldane'spseudopotentials
10.8thelaughlinwavefunction
10.8.1amosteleganteducatedguess
10.8.2theclassicalplasmaanalogy
10.8.3structurefactorandsumrules
10.8.4interpolationformulafortheenergy
10.9fractionallychargedquasiparticles
10.10thefractionalquantumhalleffect
10.11observationofthefractionalcharge
10.12incompressibilityofthequantumhallliquid
10.13neutralexcitations
10.13.1thesinglemodeapproximation
10.13.2effectiveelasticitytheory
10.13.3bosonization
10.14thespectralfunction
10.14.1anexactsumrule
10.14.2independentbosontheory
10.15chern-simonstheory
10.15.1formulationandmeanfieldtheory
10.15.2electromagneticresponseofcompositeparticles
10.16compositefermions
10.17thehalf-fi！ledstate
10.18therealityofcompositefermions
10.19wignercrystalandthestripephase
10.20edgestatesanddynamics
10.20.1sharpedgesvssmoothedges
10.20.2electrostaticsofedgechannels
10.20.3collectivemodesattheedge
10.20.4thechirailuttingerliquid
10.20.5tunnelingandtransport
exercises
appendices
appendix1fouriertransformofthecoulombinteractioninlowdimensionalsystems
appendix2second-quantizedrepresentationofsomeusefuloperators
appendix3normalorderingandwick'stheorem
appendix4thepaircorrelationfunctionandthestructurefactor
appendix5calculationoftheenergyofawignercrystalviatheewaidmethod
appendix6exactlowerboundontheground-stateenergyofthejelliummodel
appendix7thedensity——densityresponsefunctioninacrystal
appendix8exampleinwhichtheisothermalandadiabaticresponsesdiffer
appendix9latticescreeningeffectsontheeffectiveelectron-electroninteraction
appendix10constructionofthestlsexchange-correlationfield
appendix11interpolationformulasforthelocalfieldfactors
appendix12realspace-timeformofthenoninteractinggreen'sfunction
appendix13calculationoftheground-stateenergyandthermodynamicpotential
appendix14spectralrepresentationandfrequencysummations
appendix15constructionofacompletesetofwavefunctions，withagivendensity
appendix16meaningofthehighestoccupiedkohn-shameigenvalueinmetals
appendix17densityfunctionalperturbationtheory
appendix18densityfunctionaltheoryatfinitetemperature
appendix19completenessofthebosonicbasissetfortheluttingermodel
appendix20proofofthedisentanglementiemma
appendix21theindependentbosontheorem
appendix22thethree-dimensionalelectrongasathighmagneticfield
appendix23densitymatricesinthelowestlandaulevel
appendix24projectioninthelowestlandaulevel
appendix25solutionoftheindependentbosonmodel
references
index
内容简介:
Theelectronliquidparadigmisatthebasisofmostofourcurrentunderstandingofthephysicalpropertiesofelectronicsystems.Quiteremarkably,thelatterarenowadaysattheintersectionofthemostexcitingareasofscience：materialsscience,quantumchem-istry,nano-electronics,biology,andquantumcomputation.Accordingly,itsimportancecanhardlybeoverestimated.Thefieldisparticularlyattractivenotonlyforthesimplicityofitsclassicformulation,butalsobecause,byitsverynature,itisstillpossibleforindividualresearchers,armedwiththoughtfulnessanddedication,andsurroundedbyasmallgroupofcollaborators,tomakedeepcontributions,inthebesttraditionof"smallscience".
目录:
preface
1introductiontotheelectronliquid
1.1ataleofmanyelectrons
1.2wheretheelectronsroam：physicalrealizationsoftheelectronliquid
1.2.1threedimensions
1.2.2twodimensions
1.2.3onedimension
1.3themodelhamiitonian
1.3.1jeiliummodel
1.3.2coulombinteractionregularization
1.3.3theelectronicdensityasthefundamentalparameter
1.4secondquantization
1.4.1fockspaceandtheoccupationnumberrepresentation
1.4.2representationofobservables
1.4.3constructionofthesecond-quantizedhamiltonian
1.5theweakcouplingregime
1.5.1thenoninteractingelectrongas
1.5.2noninteractingspinpolarizedstates
1.5.3theexchangeenergy
1.5.4exchangeenergyinspinpolarizedstates
1.5.5exchangeandthepaircorrelationfunction
1.5.6all-ordersperturbationtheory：therpa
1.6thewignercrystal
1.6.1classicalelectrostaticenergy
1.6.2zero-pointmotion
1.7phasediagramoftheelectronliquid
1.7.1thequantummontecarloapproach
1.7.2theground-stateenergy
1.7.3experimentalobservationoftheelectrongasphases
1.7.4exoticphasesoftheelectronliquid
1.8equilibriumpropertiesoftheelectronliquid
1.8.1pressure，compressibility，andspinsusceptibility
1.8.2thevirialtheorem
1.8.3theground-stateenergytheorem
exercises

2thehartree——fockapproximation
2.1introduction
2.2formulationofthehartree-focktheory
2.2.1thehartree-fockeffectivehamiltonian
2.2.2thehartree-fockequations
2.2.3ground-stateandexcitationenergies
2.2.4twostabilitytheoremsandthecoulombgap
2.3hartree-fockfactorizationandmeanfieldtheory
2.4applicationtotheuniformelectrongas
2.4.1theexchangeenergy
2.4.2polarizedversusunpolarizedstates
2.4.3compressibilityandspinsusceptibility
2.5stabilityofhartree——fockstates
2.5.1basicdefinitions：localversusglobalstability
2.5.2localstabilitytheory
2.5.3localandglobalstabilityforauniformlypolarizedelectrongas
2.6spindensitywaveandchargedensitywavehartree-fockstates
2.6.1hartree-focktheoryofspiralspindensitywaves
2.6.2spindensitywaveinstabilitywithcontactinteractionsinonedimension
2.6.3proofofoverhauser'sinstabilitytheorem
2.7bcsnonnumber-conservingmeanfieldtheory
2.8localapproximationstotheexchange
2.8.1slater'slocalexchangepotential
2.8.2theoptimizedeffectivepotential
2.9real-worldhartree-focksystems
exercises

3linearresponsetheory
3.1introduction
3.2generaltheoryoflinearresponse
3.2.1responsefunctions
3.2.2periodicperturbations
3.2.3exacteigenstatesandspectralrepresentations
3.2.4symmetryandreciprocityrelations
3.2.5originofdissipation
3.2.6time-dependentcorrelationsandthefiuctuation——dissipationtheorem
3.2.7analyticpropertiesandcollectivemodes
3.2.8sumrules.
3.2.9thestiffnesstheorem
3.2.10bogoliubovinequality
3.2.11adiabaticversusisothermalresponse
3.3densityresponse
3.3.1thedensity——densityresponsefunction
3.3.2thedensitystructurefactor
3.3.3high-frequencybehaviorandsumrules
3.3.4thecompressibilitysumrule
3.3.5totalenergyanddensityresponse
3.4currentresponse
3.4.1thecurrent——currentresponsefunction
3.4.2gaugeinvariance
3.4.3theorbitalmagneticsusceptibility
3.4.4electricalconductivity：conductorsversusinsulators
3.4.5thethirdmomentsumrule
3.5spinresponse
3.5.1densityandlongitudinalspinresponse
3.5.2high-frequencyexpansion
3.5.3transversespinresponse
exercises

4linearresponseofindependentelectrons
4.1introduction
4.2linearresponseformalismfornon-interactingelectrons
4.3densityandspinresponsefunctions
4.4thelindhardfunction
4.4.1thestaticlimit
4.4.2theelectron-holecontinuum
4.4.3thenatureofthesingularityatsmallqandto
4.4.4thelindhardfunctionatfinitetemperature
4.5transversecurrentresponseandlandaudiamagnetism
4.6elementarytheoryofimpurityeffects
4.6.1derivationofthedrudeconductivity
4.6.2thedensity-densityresponsefunctioninthepresenceofimpurities
4.6.3thediffusionpole
4.7meanfieldtheoryoflinearresponse
exercises

5linearresponseofaninteractingelectronliquid
5.1introductionandguidetothechapter
5.2screenedpotentialanddielectricfunction
5.2.1thescalardielectricfunction
5.2.2properversusfulldensityresponseandthecompressibilitysumrule
5.2.3compressibilityfromcapacitance
5.3therandomphaseapproximation
5.3，1therpaastime-dependenthartreetheory
5.3.2staticscreening
5.3.3plasmons
5.3.4theelectron-holecontinuuminrpa
5.3.5thestaticstructurefactorandthepaircorrelationfunction
5.3.6therpaground-stateenergy
5.3.7critiqueoftherpa
5.4themany-bodylocalfieldfactors
5.4.1localfieldfactorsandresponsefunctions
5.4.2many-bodyenhancementofthecompressibilityandthespinsusceptibility
5.4.3staticresponseandfriedeloscillations
5.4.4thestlsscheme
5.4.5multicomponentandspin-polarizedsystems
5.4.6currentandtransversespinresponse
5.5effectiveinteractionsintheelectronliquid
5.5.1testcharge——testchargeinteraction
5.5.2electron-testchargeinteraction
5.5.3electron-electroninteraction
5.6exactpropertiesofthemany-bodylocalfieldfactors
5.6.1wavevectordependence
5.6.2frequencydependence
5.7theoriesofthedynamicallocalfieldfactor
5.7.1thetime-dependenthartree-fockapproximation
5.7.2firstorderperturbationtheoryandbeyond
5.7.3themode-decouplingapproximation
5.8calculationofobservableproperties
5.8.1plasmondispersionanddamping
5.8.2dynamicalstructurefactor
5.9generalizedelasticitytheory
5.9.1elasticityandhydrodynamics
5.9.2visco-elasticconstantsoftheelectronliquid
5.9.3spindiffusion
exercises

6theperturbativecalculationoflinearresponsefunctions
6.1introduction
6.2zero-temperatureformalism
6.2.1time-orderedcorrelationfunction
6.2.2theadiabaticconnection
6.2.3thenon-interactinggreen'sfunction
6.2.4diagrammaticperturbationtheory
6.2.5fouriertransformation
6.2.6translationa！iyinvariantsystems
6.2.7diagrammaticcalculationofthelindhardfunction
6.2.8first-ordercorrectiontothedensity-densityresponsefunction
6.3integralequationsindiagrammaticperturbationtheory
6.3.1properresponsefunctionandscreenedinteraction
6.3.2green'sfunctionandself-energy
6.3.3skeletondiagrams
6.3.4irreducibleinteractions
6.3.5self-consistentequations
6.3.6two-bodyeffectiveinteraction：thelocalapproximation
6.3..7extensiontobrokensymmetrystates
6.4perturbationtheoryatfinitetemperature
exercises

7densityfunctionaltheory
7.1introduction
7.2ground-stateformalism
7.2.1thevariationalprincipleforthedensity
7.2.2thehohenberg-kohntheorem
7.2.3thekohn——shamequation
7.2.4meaningofthekohn-shameigenvalues
7.2.5theexchange-correlationenergyfunctional
7.2.6exactpropertiesofenergyfunctionals
7.2.7systemswithvariableparticlenumber
7.2.8derivativediscontinuitiesandthebandgapproblem
7.2.9generalizeddensityfunctionaltheories
7.3approximatefunctionais
7.3.1thethomas-fermiapproximation
7.3.2thelocaldensityapproximationfortheexchange-correlationpotential
7.3.3thegradientexpansion
7.3.4generalizedgradientapproximation
7.3.5vanderwaalsfunctionals
7.4currentdensityfunctionaltheory
7.4.1thevorticityvariable
7.4.2thekohn-shamequation
7.4.3magneticscreening
7.4.4thelocaldensityapproximation
7.5time-dependentdensityfunctionaltheory
7.5.1therunge——grosstheorem
7.5.2thetime-dependentkohn-shamequation
7.5.3adiabaticapproximation
7.5.4frequency-dependentlinearresponse
7.6thecalculationofexcitationenergies
7.6.1finitesystems
7.6.2infinitesystems
7.7reasonforthesuccessoftheadiabaticlda
7.8beyondtheadiabaticapproximation
7.8.1thezero-forcetheorem
7.8.2the"ultra-nonlocality"problem
7.9currentdensityfunctionaltheoryandgeneralizedhydrodynamics
7.9.1thexcvectorpotentialinahomogeneouselectronliquid
7.9.2theexchange-correlationfieldintheinhomogeneouselectronliquid
7.9.3thepolarizabilityofinsulators
7.9.4spincurrentdensityfunctionaltheory
7.9.5linewidthofcollectiveexcitations
7.9.6nonlinearextensions
exercises

8thenormalfermiliquid
8.1introductionandoverviewofthechapter
8.2thelandaufermiliquid
8.3macroscopictheoryoffermiliquids
8.3.1thelandauenergyfunctional
8.3.2theheatcapacity
8.3.3thelandaufermiliquidparameters
8.3.4thecompressibility
8.3.5theparamagneticspinresponse
8.3.6theeffectivemass
8.3.7theeffectsoftheelectron-phononcoupling
8.3.8measuringm*，k，g*andxs
8.3.9thekineticequation
8.3.10theshearmodulus
8.4simpletheoryofthequasiparticlelifetime
8.4.1generalformulas
8.4.2three-dimensionalelectrongas
8.4.3two-dimensionalelectrongas
8.4.4exchangeprocesses
8.5microscopicunderpinningofthelandautheory
8.5.1thespectralfunction
8.5.2themomentumoccupationnumber
8.5.3quasiparticleenergy，renormalizationconstant，andeffectivemass
8.5.4luttinger'stheorem
8.5.5thelandauenergyfunctional
8.6therenormalizedhamiitonianapproach
8.6.1separationofslowandfastdegreesoffreedom
8.6.2eliminationofthefastdegreesoffreedom
8.6.3thequasiparticlehamiltonian
8.6.4thequasiparticleenergy
8.6.5physicalsignificanceoftherenormalizedhamiltonian
8.7approximatecalculationsoftheself-energy
8.7.1thegwapproximation
8.7.2diagrammaticderivationofthegeneralizedgwseif-energy
8.8calculationofquasiparticleproperties
8.9superconductivitywithoutphonons?
8.10thedisorderedelectronliquid
8.10.1thequasiparticlelifetime
8.10.2thedensityofstates
8.10，3coulomblifetimesandweaklocalizationintwo-dimensionalmetals
exercises

9electronsinonedimensionandtheluttingerliquid
9.1non-fermiliquidbehavior
9.2theluttingermodel
9.3theanomalouscommutator
9.4introducingthebosons
9.5solutionoftheluttingermodel
9.5.1exactdiagonalization
9.5.2physicalproperties
9.6bosonizationofthefermions
9.6.1constructionofthefermionfields
9.6.2commutationrelations
9.6.3constructionofobservables
9.7thegreen'sfunction
9.7.1analyticalformulation
9.7.2evaluationoftheaverages
9.7.3non-interactinggreen'sfunction
9.7.4asymptoticbehavior
9.8thespectralfunction
9.9themomentumoccupationnumber
9.10densityresponsetoashort-rangeimpurity
9.1！theconductanceofaluttingerliquid
9.12spin-chargeseparation
9.13long-rangeinteractions
exercises

10thetwo-dimensionalelectronliquidathighmagneticfield
10.1introductionandoverview
10.2one-electronstatesinamagneticfield
10.2.1energyspectrum
10.2.2one-electronwavefunctions
10.2.3fock-darwinlevels
10.2.4lowestlandaulevel
10.2.5coherentstates
10.2.6effectofanelectricfield
10.2.7slowlyvaryingpotentialsandedgestates
10.3theintegralquantumhalleffect
10.3.1phenomenology
10.3.2the"edgestate"approach
10.3.3stredaformula
10.3.4thelaughlinargument
10.4electronsinfulllandaulevels：energetics
10.4.1noninteractingkineticenergy
10.4.2densitymatrix
10.4.3paircorrelationfunction
10.4.4exchangeenergy
10.4.5the"lindhard"function
10.4.6staticscreening
10.4.7correlationenergy-therandomphaseapproximation
10.4.8fractionalfillingfactors
10.5exchange-driventransitionsintiltedfield
10.6electronsinfulllandaulevels：dynamics
10.6.1classificationofneutralexcitations
10.6.2collectivemodes
10.6.3time-dependenthartree-focktheory
10.6.4kohn'stheorem
10.7electronsinthelowestlandaulevel
10.7.1onefulllandaulevel
10.7.2two-particlestates：haldane'spseudopotentials
10.8thelaughlinwavefunction
10.8.1amosteleganteducatedguess
10.8.2theclassicalplasmaanalogy
10.8.3structurefactorandsumrules
10.8.4interpolationformulafortheenergy
10.9fractionallychargedquasiparticles
10.10thefractionalquantumhalleffect
10.11observationofthefractionalcharge
10.12incompressibilityofthequantumhallliquid
10.13neutralexcitations
10.13.1thesinglemodeapproximation
10.13.2effectiveelasticitytheory
10.13.3bosonization
10.14thespectralfunction
10.14.1anexactsumrule
10.14.2independentbosontheory
10.15chern-simonstheory
10.15.1formulationandmeanfieldtheory
10.15.2electromagneticresponseofcompositeparticles
10.16compositefermions
10.17thehalf-fi！ledstate
10.18therealityofcompositefermions
10.19wignercrystalandthestripephase
10.20edgestatesanddynamics
10.20.1sharpedgesvssmoothedges
10.20.2electrostaticsofedgechannels
10.20.3collectivemodesattheedge
10.20.4thechirailuttingerliquid
10.20.5tunnelingandtransport
exercises
appendices
appendix1fouriertransformofthecoulombinteractioninlowdimensionalsystems
appendix2second-quantizedrepresentationofsomeusefuloperators
appendix3normalorderingandwick'stheorem
appendix4thepaircorrelationfunctionandthestructurefactor
appendix5calculationoftheenergyofawignercrystalviatheewaidmethod
appendix6exactlowerboundontheground-stateenergyofthejelliummodel
appendix7thedensity——densityresponsefunctioninacrystal
appendix8exampleinwhichtheisothermalandadiabaticresponsesdiffer
appendix9latticescreeningeffectsontheeffectiveelectron-electroninteraction
appendix10constructionofthestlsexchange-correlationfield
appendix11interpolationformulasforthelocalfieldfactors
appendix12realspace-timeformofthenoninteractinggreen'sfunction
appendix13calculationoftheground-stateenergyandthermodynamicpotential
appendix14spectralrepresentationandfrequencysummations
appendix15constructionofacompletesetofwavefunctions，withagivendensity
appendix16meaningofthehighestoccupiedkohn-shameigenvalueinmetals
appendix17densityfunctionalperturbationtheory
appendix18densityfunctionaltheoryatfinitetemperature
appendix19completenessofthebosonicbasissetfortheluttingermodel
appendix20proofofthedisentanglementiemma
appendix21theindependentbosontheorem
appendix22thethree-dimensionalelectrongasathighmagneticfield
appendix23densitymatricesinthelowestlandaulevel
appendix24projectioninthelowestlandaulevel
appendix25solutionoftheindependentbosonmodel
references
index

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