随机矩阵在物理学中的应用

(德) 布拉钦 (Brezin,E.) 等, 编著

出版社：科学出版社

年代：2008

定价：88.0

书籍简介:

随机矩阵在物理上被广泛采用将近60～70年，起源于Dyson和wingner的著作。虽然这是一个老课题，但随着它不断的发展成为物理学和数学的一个新领域。由随机矩阵理论所启发数学方法正在变得更加强大，更尖端，并迅速发展了物理上的应用。

书籍目录:

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

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出版地	北京	出版单位	科学出版社
版次	影印本	印次	1
定价(元)	88.0	语种	英文
尺寸	24	装帧	精装
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随机矩阵在物理学中的应用是科学出版社于2008.出版的中图分类号为 O4 的主题关于随机矩阵－应用－物理学－英文的书籍。