国外物理名著系列20：随机矩阵在物理学中的应用（影印版）

图书标准信息

• 作者 [德]布拉钦 著
• 出版社 科学出版社
• 出版时间 2008-08
• 版次 1
• ISBN 9787030226266
• 定价 98.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 513页
• 字数 631千字
• 正文语种 英语

【内容简介】

　　Dyson和Wigner最先成功地将随机矩阵应用到物理学中，经过六七十年的发展，现在它在物理学中的应用越来越广泛，并且已经渗透到了现代数学、物理学的很多新兴领域，是理论物理学家的重要数学工具。随机矩阵理论相关的数学方法能够解决更多的问题，而且方式更加灵活，在物理学中的应用也更加深入，可以用来计算介观系统的通用关系。它在无序系统和量子混沌领域也有一些新的应用，并且通过建立新的矩阵模型，在二维引力和弦以及非阿贝尔规范理论方面取得了重要进展。
　　本书由本领域的杰出学者撰写，系统阐述了相关的理论知识。适合对随机矩阵处理物理问题感兴趣的研究生和科研人员参考。

【目录】

Preface
RandomMatricesandNumberTheory
J.P.Keating
1Introduction
2ζ(1/2+it)andlogζ(1/2+it)
3Characteristicpolynomialsofrandomunitarymatrices
4Othercompactgroups
5FamiliesofL-functionsandsymmetry
6Asymptoticexpansions
References

2DQuantumGravity，MatrixModelsandGraphCombinatorics
P.DiFrancesco
1Introduction
2Matrixmodelsfor2Dquantumgravity
3Theone-matrixmodelI：largeNlimitandtheenumerationofplanargraphs
4Thetreesbehindthegraphs
5Theone-matrixmodelII：topologicalexpansionsandquantumgravity58
6Thecombinatoricsbeyondmatrixmodels：geodesicdistanceinplanargraphs
7Planargraphsasspatialbranchingprocesses
8Conclusion
References
EigenvalueDynamics，FollytonsandLargeNLimitsofMatrices
JoakimArnlind，JensHoppe
References

RandomMatricesandSupersymmetryinDisorderedSystems
K.B.Efetov
1Supersymmetrymethod
2Wavefunctionsfluctuationsinafinitevolume.Multifractality
3Recentandpossiblefuturedevelopments
4Summary
Acknowledgements
References

HydrodynamicsofCorrelatedSystems
AlexanderG．Abanoy
1Introduction
2Instantonorrarefluctuationmethod
3Hydrodynamicapproach
4Linearizedhydrodynamicsorbosoflization
5EFPthroughanasymptoticsofthesolution
6Freefermions
7Calogero-Sutherlandmodel
8Freefermionsonthelattice
9Conclusion
Acknowledgements
Appendix：Hydrodynamicapproachtonon-Galileaninvariantsystems
Appendix：ExactresultsforEFPinsomeintegrablemodels
References

QCD，ChiralRandomMatrixTheoryandIntegrability
J．JM．Verbaarschot
1Summarv
2IntrodUCtion
3OCD
4TheDiracspectruminQCD
5LoweflergylimitofQCD
6ChiralRMTandtheQCDDiracspectrum
7IntegrabilityandtheQCDpartitionfunction
8QCDatfinitebaryondensity
9FullQCDatnonzerochemicalpotential
10Conclusions
Acknowledgements
References

EUClideanRandomMatrices：SOlvedandOpenProblems
GiorgioParisi
1Introduction
2Basicdefinitions
3Physicalmotivations
4Fieldtheory
5Thesimplestcase
6Phonons
References

MatrixModelsandGrowthProcesses3
A．Zabrodin
1Introduction
2Someensemblesofrandommatriceswithcornplexeigenvalues
3ExactresultsatfiniteN
4LargeNlimit
5Thematrixmodelasagrowthproblem
References

MatrixModelsandTopologicalStrings
MarcosMarino
1Introduction
2Matrixmodels
3TypeBtopologicalstringsandmatrixmodels
4TypeAtopologicalstrings，Chern-Simonstheoryandmatrixmodels366
References

MatrixModelsofModuliSpace
SunilMukhi
1Introduction
2ModulispaceofRiemannsurfacesanditstopology
3Quadraticdifferentialsandfatgraphs
4ThePennermodel
5Pennermodelandmatrixgammafunction
6TheKontsevichModel
7Applicationstostringtheory
8Conclusions
References

MatrixModelsand2DStringTheory
EmilJ.Martinec
1Introduction
2Anoverviewofstringtheory
3StringsinD-dimensionalspacetime
4Discretizedsurfacesand2Dstringtheory
5Anoverviewofobservables
6Samplecalculation：thediskone-pointfunction
7Worldsheetdescriptionofmatrixeigenvalues
8Furtherresults
9Openproblems
References

MatrixModelsasConformalFieldTheories
IvanK.Kostov
1Introductionandhistoricalnotes
2Hermitianmatrixintegral：saddlepointsandhyperellipticcurves
3ThehermitianmatrixmodelasachiralCFT
4Quasiclassicalexpansion：CFTonahyperellipticRiemannsurface
5Generalizationtochainsofrandommatrices
References

LargeNAsymptoticsofOrthogonalPolynomialsfromIntegrabilitytoAlgebraicGeometry
B.Eynard
1Introduction
2Definitions
3Orthogonalpolynomials
4Differentialequationsandintegrability
5Riemann-Hilbertproblemsandisomonodromies
6WKB-likeasymptoticsandspectralcurve
7Orthogonalpolynomialsasmatrixintegrals
8ComputationofderivativesofF(0)
9Saddlepointmethod
10Solutionofthesaddlepointequation
11Asymptoticsoforthogonalpolynomials
12Conclusion
References