Symmetry classes in random matrix theory
作者： Martin R. Zirnbauer
DOI:
关键词: Random matrix 、 Extension (predicate logic) 、 Centrosymmetric matrix 、 Matrix (mathematics) 、 Hamiltonian matrix 、 Symmetric matrix 、 Pascal matrix 、 Symmetry (geometry) 、 Theoretical physics 、 Mathematics 、 Discrete mathematics
摘要: Dyson's (1962) classification of matrix ensembles is reviewed from a modern perspective, and its recent extension to disordered fermion problems motivated described. It explained in particular why symmetry classes are associated with large families symmetric spaces.
arxiv.org
harvard.edu参考文章(4)
Hermann Weyl, The Classical Groups The Mathematical Gazette. ,vol. 24, pp. 216- ,(1947) , 10.1515/9781400883905
Sigurdur Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces ,(1978)
Freeman J. Dyson, The Threefold Way. Algebraic Structure of Symmetry Groups and Ensembles in Quantum Mechanics Journal of Mathematical Physics. ,vol. 3, pp. 1199- 1215 ,(1962) , 10.1063/1.1703863
Jacobus Verbaarschot, Spectrum of the QCD Dirac operator and chiral random matrix theory. Physical Review Letters. ,vol. 72, pp. 2531- 2533 ,(1994) , 10.1103/PHYSREVLETT.72.2531