Regularity versus randomness in matrix-element distributions in quantum nonintegrable Hamiltonian systems. II. Colored random matrix as a phenomenological model for level statistics of many-degree-of-freedom Hamiltonian systems

Abstract

A class of colored (non-δ-correlated) random matrices composed of two independent systems of random number sequences, each of which is allocated to diagonal and off-diagonal parts of the matrices, is studied as workable models for the analysis of level statistics of sufficiently large degree-of-freedom Hamiltonian systems. In band random-matrix models, the rapid saturation toward the Wigner-type distribution as a function of the bandwidth is observed in spacing distribution patterns, suggesting that colored random matrices are capable of reproducing the non-δ-correlated random property found in level-spacing characteristics of real Hamiltonian systems. Detailed analysis reveals that at least two system parameters characterizing the colored random matrices are necessary for a workable basis of the model. The effect of the variance around the mean value of random number sequences on the spacing distribution is investigated in the small-bandwidth region, and a new type of anomalous distribution with non-Wigner-like distribution patterns is found in the small-variance limit.