Integrable random matrix ensembles

被引：18
|
作者：
Bogomolny, E. [1 ]
Giraud, O. [1 ]
Schmit, C. [1 ]
机构：
[1] Univ Paris 11, CNRS, LPTMS, UMR8626, F-91405 Orsay, France
来源：
NONLINEARITY | 2011年 / 24卷 / 11期
关键词：
ACTION-ANGLE MAPS; INTERMEDIATE SPECTRAL STATISTICS; SCATTERING-THEORY; SYSTEMS; TRANSITION; SOLITONS;
D O I：
10.1088/0951-7715/24/11/010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We propose new classes of random matrix ensembles whose statistical properties are intermediate between statistics of Wigner-Dyson random matrices and Poisson statistics. The construction is based on integrable N-body classical systems with a random distribution of momenta and coordinates of the particles. The Lax matrices of these systems yield random matrix ensembles whose joint distribution of eigenvalues can be calculated analytically thanks to the integrability of the underlying system. Formulae for spacing distributions and level compressibility are obtained for various instances of such ensembles.
引用
收藏
页码：3179 / 3213
页数：35
相关论文
共 50 条
  • [41] Fluctuations of the spectrum in rotationally invariant random matrix ensembles
    Meckes, Elizabeth S.
    Meckes, Mark W.
    [J]. RANDOM MATRICES-THEORY AND APPLICATIONS, 2021, 10 (03)
  • [42] Random matrix ensembles associated to compact symmetric spaces
    Dueñez, E
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 244 (01) : 29 - 61
  • [43] Conditional random matrix ensembles and the stability of dynamical systems
    Kirk, Paul
    Rolando, Delphine M. Y.
    MacLean, Adam L.
    Stumpf, Michael P. H.
    [J]. NEW JOURNAL OF PHYSICS, 2015, 17
  • [44] The Limiting Characteristic Polynomial of Classical Random Matrix Ensembles
    Chhaibi, Reda
    Hovhannisyan, Emma
    Najnudel, Joseph
    Nikeghbali, Ashkan
    Rodgers, Brad
    [J]. ANNALES HENRI POINCARE, 2019, 20 (04): : 1093 - 1119
  • [45] Random Matrix Ensembles Associated to Compact Symmetric Spaces
    Eduardo Dueñez
    [J]. Communications in Mathematical Physics, 2004, 244 : 29 - 61
  • [46] Random matrix ensembles for semi-separable systems
    Prosen, T
    Seligman, TH
    Weidenmüller, HA
    [J]. EUROPHYSICS LETTERS, 2001, 55 (01): : 12 - 18
  • [47] Arbitrary unitarily invariant random matrix ensembles and supersymmetry
    Guhr, Thomas
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (42): : 13191 - 13223
  • [48] Poisson statistics for the largest eigenvalues in random matrix ensembles
    Soshnikov, Alexander
    [J]. MATHEMATICAL PHYSICS OF QUANTUM MECHANICS: SELECTED AND REFEREED LECTURES FROM QMATH9, 2006, 690 : 351 - 364
  • [49] Inner structure of vehicular ensembles and random matrix theory
    Krbalek, Milan
    Hobza, Tomas
    [J]. PHYSICS LETTERS A, 2016, 380 (21) : 1839 - 1847
  • [50] Random matrix ensembles with column/row constraints: II
    Sadhukhan, Suchetana
    Shukla, Pragya
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2015, 48 (41)
12345