随机矩阵在物理学中的应用-(影印版) 节选

Dyson和Wigner*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。《随机矩阵在物理学中的应用》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。

随机矩阵在物理学中的应用-(影印版) 目录

PrefaceRandom Matrices and Number TheoryJ.P. Keating1 Introduction2 ζ(1/2+it)and logζ(1/2+it)3 Characteristic polynomials of random unitary matrices4 Other compact groups5 Families of L-functions and symmetry6 Asymptotic expansionsReferences2D Quantum Gravity, Matrix Models and Graph CombinatoricsP. Di Francesco1 Introduction2 Matrix models for 2D quantum gravity3 The one-matrix model I: large N limit and the enumeration of planar graphs4 The trees behind the graphs5 The one-matrix model II：topological expansions and quantum gravity 586 The combinatorics beyond matrix models: geodesic distance in planar graphs7 Planar graphs as spatial branching processes8 ConclusionReferencesEigenvalue Dynamics, Follytons and Large N Limits of MatricesJoakim Arnlind, Jens HoppeReferencesRandom Matrices and Supersymmetry in Disordered SystemsK.B. Efetov1 Supersymmetry method2 Wave functions fluctuations in a finite volume. Multifractality3 Recent and possible future developments4 SummaryAcknowledgementsReferencesHydrodynamics of Correlated SystemsAlexander G．Abanoy1 Introduction2 Instanton or rare fluctuation method3 Hydrodynam ic approach4 Linearized hydrodynamics or bosoflization5 EFP through an asymptotics of the solution6 Free fermions7 Calogero-Sutherland model8 Free fermions on the lattice9 ConclusionAcknowledgementsAppendix：Hydrodynamic approach to non-Galilean invariant systemsAppendix：Exact results for EFP in some integrable modelsReferencesQCD，Chiral Random Matrix Theory and IntegrabilityJ．JM．Verbaarschot1 Summarv2 IntrodUCtion3 OCD4 The Dirac spectrum in QCD5 Low eflergy limit of QCD6 Chiral RMT and the QCD Dirac spectrum7 Integrability and the QCD partition function8 QCD at fin ite baryon density9 Full QCD at nonzero chemical potential10 ConclusionsAcknowledgementsReferencesEUClidean Random Matrices：SOlved and Open ProblemsGiorgio Parisi1 Introduction2 Basic definitions3 Physical motivations4 Field theory5 The simplest case6 PhononsReferencesMatrix Models and Growth Processes3A．Zabrodin1 Introduction2 Some ensembles of random matrices with cornplex eigenvalues3 Exact results at finite N4 Large N limit5 The matrix model as a growth problemReferencesMatrix Models and Topological StringsMarcos Marino1 Introduction2 Matrix models3 Type B topological strings and matrix models4 Type A topological strings, Chern-Simons theory and matrix models 366ReferencesMatrix Models of Moduli SpaceSunil Mukhi1 Introduction2 Moduli space of Riemann surfaces and its topology3 Quadratic differentials and fatgraphs4 The Penner model5 Penner model and matrix gamma function6 The Kontsevich Model7 Applications to string theory8 ConclusionsReferencesMatrix Models and 2D String TheoryEmil J. Martinec1 Introduction2 An overview of string theory3 Strings in D-dimensional spacetime4 Discretized surfaces and 2D string theory5 An overview of observables6 Sample calculation: the disk one-point function7 Worldsheet description of matrix eigenvalues8 Further results9 Open problemsReferencesMatrix Models as Conformal Field TheoriesIvan K. Kostov1 Introduction and historical notes2 Hermitian matrix integral: saddle points and hyperelliptic curves3 The hermitian matrix model as a chiral CFT4 Quasiclassical expansion: CFT on a hyperelliptic Riemann surface5 Generalization to chains of random matricesReferencesLarge N Asymptotics of Orthogonal Polynomials from Integrability to Algebraic GeometryB. Eynard1 Introduction2 Definitions3 Orthogonal polynomials4 Differential equations and integrability5 Riemann-Hilbert problems and isomonodromies6 WKB-like asymptotics and spectral curve7 Orthogonal polynomials as matrix integrals8 Computation of derivatives of F(0)9 Saddle point method10 Solution of the saddlepoint equation11 Asymptotics of orthogonal polynomials12 ConclusionReferences