随机矩阵在物理学中的应用
点此进入淘宝搜索页搜索分類: 图书,自然科学,物理学,理论物理学,
作者： （德）布拉钦等编著
出 版 社： 科学出版社
出版时间： 2008-8-1字数： 631000版次： 1页数： 513印刷时间： 2008/08/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9787030226266包装： 精装内容简介
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
Random Matrices and Number Theory
J.P. Keating
1 Introduction
2 ζ(1/2+it)and logζ(1/2+it)
3 Characteristic polynomials of random unitary matrices
4 Other compact groups
5 Families of L-functions and symmetry
6 Asymptotic expansions
References
2D Quantum Gravity, Matrix Models and Graph Combinatorics
P. Di Francesco
1 Introduction
2 Matrix models for 2D quantum gravity
3 The one-matrix model I: large N limit and the enumeration of planar graphs
4 The trees behind the graphs
5 The one-matrix model II：topological expansions and quantum gravity 58
6 The combinatorics beyond matrix models: geodesic distance in planar graphs
7 Planar graphs as spatial branching processes
8 Conclusion
References
Eigenvalue Dynamics, Follytons and Large N Limits of Matrices
Joakim Arnlind, Jens Hoppe
References
Random Matrices and Supersymmetry in Disordered Systems
K.B. Efetov
1 Supersymmetry method
2 Wave functions fluctuations in a finite volume. Multifractality
3 Recent and possible future developments
4 Summary
Acknowledgements
References
Hydrodynamics of Correlated Systems
Alexander G．Abanoy
1 Introduction
2 Instanton or rare fluctuation method
3 Hydrodynam ic approach
4 Linearized hydrodynamics or bosoflization
5 EFP through an asymptotics of the solution
6 Free fermions
7 Calogero-Sutherland model
8 Free fermions on the lattice
9 Conclusion
Acknowledgements
Appendix：Hydrodynamic approach to non-Galilean invariant systems
Appendix：Exact results for EFP in some integrable models
References
QCD，Chiral Random Matrix Theory and Integrability
J．JM．Verbaarschot
1 Summarv
2 IntrodUCtion
3 OCD
4 The Dirac spectrum in QCD
5 Low eflergy limit of QCD
6 Chiral RMT and the QCD Dirac spectrum
7 Integrability and the QCD partition function
8 QCD at fin ite baryon density
9 Full QCD at nonzero chemical potential
10 Conclusions
Acknowledgements
References
EUClidean Random Matrices：SOlved and Open Problems
Giorgio Parisi
1 Introduction
2 Basic definitions
3 Physical motivations
4 Field theory
5 The simplest case
6 Phonons
References
Matrix Models and Growth Processes3
A．Zabrodin
1 Introduction
2 Some ensembles of random matrices with cornplex eigenvalues
3 Exact results at finite N
4 Large N limit
5 The matrix model as a growth problem
References
Matrix Models and Topological Strings
Marcos Marino
1 Introduction
2 Matrix models
3 Type B topological strings and matrix models
4 Type A topological strings, Chern-Simons theory and matrix models 366
References
Matrix Models of Moduli Space
Sunil Mukhi
1 Introduction
2 Moduli space of Riemann surfaces and its topology
3 Quadratic differentials and fatgraphs
4 The Penner model
5 Penner model and matrix gamma function
6 The Kontsevich Model
7 Applications to string theory
8 Conclusions
References
Matrix Models and 2D String Theory
Emil J. Martinec
1 Introduction
2 An overview of string theory
3 Strings in D-dimensional spacetime
4 Discretized surfaces and 2D string theory
5 An overview of observables
6 Sample calculation: the disk one-point function
7 Worldsheet description of matrix eigenvalues
8 Further results
9 Open problems
References
Matrix Models as Conformal Field Theories
Ivan K. Kostov
1 Introduction and historical notes
2 Hermitian matrix integral: saddle points and hyperelliptic curves
3 The hermitian matrix model as a chiral CFT
4 Quasiclassical expansion: CFT on a hyperelliptic Riemann surface
5 Generalization to chains of random matrices
References
Large N Asymptotics of Orthogonal Polynomials from Integrability to Algebraic Geometry
B. Eynard
1 Introduction
2 Definitions
3 Orthogonal polynomials
4 Differential equations and integrability
5 Riemann-Hilbert problems and isomonodromies
6 WKB-like asymptotics and spectral curve
7 Orthogonal polynomials as matrix integrals
8 Computation of derivatives of F(0)
9 Saddle point method
10 Solution of the saddlepoint equation
11 Asymptotics of orthogonal polynomials
12 Conclusion
References
