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


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