標題: | Level statistics of Hessian matrices: random matrices with conservation constraints |
作者: | Ma, WJ Wu, TM Hsieh, J Chang, SL 物理研究所 Institute of Physics |
關鍵字: | Hessian;random matrices;GOE;level statistics |
公開日期: | 1-四月-2003 |
摘要: | 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 round 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. (C) 2002 Published by Elsevier Science B.V. |
URI: | http://dx.doi.org/10.1016/S0378-4371(02)01796-X http://hdl.handle.net/11536/28001 |
ISSN: | 0378-4371 |
DOI: | 10.1016/S0378-4371(02)01796-X |
期刊: | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS |
Volume: | 321 |
Issue: | 1-2 |
起始頁: | 364 |
結束頁: | 368 |
顯示於類別: | 會議論文 |