Gaussian ensembles of random hermitian matrices intermediate between orthogonal and unitary ones

A Gaussian ensemble of Hermitian matrices depending on a parameter α is considered. When α=0, the ensemble is Gaussian Orthogonal, and when α=1, it is Gaussian Unitary. An analytic expression for then-level correlation and cluster functions is given for anyn and 0≦α≦1. This ensemble is of relevance in the study of time reversal symmetry breaking of nuclear interactions.

[1]  C. Itzykson.  The planar approximation , 1980 .

[2]  J. F. McDonald,et al.  Possibility of Detecting a Small Time-Reversal-Noninvariant Term in the Hamiltonian of a Complex System by Measurements of Energy-Level Spacings , 1967 .

[3]  F. Dyson.  Correlations between eigenvalues of a random matrix , 1970 .

[4]  C. Itzykson,et al.  The planar approximation. II , 1980 .

[5]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[6]  A. Pandey.  Statistical properties of many-particle spectra. IV. New ensembles by Stieltjes transform methods☆ , 1981 .

[7]  A. Pandey.  Statistical properties of many-particle spectra : III. Ergodic behavior in random-matrix ensembles , 1979 .

[8]  O. Bohigas,et al.  Fluctuation properties of nuclear energy levels: Do theory and experiment agree? , 1982 .

[9]  P. A. Mello,et al.  Random matrix physics: Spectrum and strength fluctuations , 1981 .

[10]  Madan Lal Mehta,et al.  Random Matrices and the Statistical Theory of Energy Levels. , 1970 .

[11]  H. Camarda.  Upper limit on a time reversal noninvariant part of Wigner's random matrix model , 1976 .

[12]  M. L. Mehta,et al.  Distribution laws for the roots of a random antisymmetric hermitian matrix , 1968 .

[13]  A. Erdélyi,et al.  Tables of integral transforms , 1955 .

[14]  M. L. Mehta,et al.  A note on correlations between eigenvalues of a random matrix , 1971 .

[15]  E. Wigner.  Random Matrices in Physics , 1967 .

[16]  F. Dyson.  Statistical Theory of the Energy Levels of Complex Systems. I , 1962 .