Level statistics of Hessian matrices: Random matrices with conservation constraints

W. J. Ma*, Ten-Ming Wu, J. Hsieh, S. L. Chang


研究成果: Conference article同行評審

2 引文 斯高帕斯(Scopus)


We consider the Hessian matrices of simple liquid systems as a new type of random matrices. By numerically comparing the distribution of the nearest-neighbor level spacing of the eigenvalues with the Wigner's surmise, we found that the level statistics is akin to the generic Gaussian Orthogonal Ensemble (GOE), in spite of the constraints due to the summation rules and the presence of the correlation among the components inherited with the underlying spatial configuration. The distribution is in good agreement with the Wigner's prediction if only the extended eigenstates are considered. Indeed, our theoretical analysis shows that the ensemble of real symmetric matrices with full randomness, but constrained by the summation rules, is equivalent to the GOE with matrices of the rank lowered by the spatial dimension.

頁(從 - 到)364-368
期刊Physica A: Statistical Mechanics and its Applications
出版狀態Published - 1 四月 2003
事件Statphys - Taiwan - 2002: Lattice Models and Complex Systems - Taipei and Taichung, Taiwan
持續時間: 26 五月 20021 六月 2002


深入研究「Level statistics of Hessian matrices: Random matrices with conservation constraints」主題。共同形成了獨特的指紋。