Level statistics of Hessian matrices: Random matrices with conservation constraints

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

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)364-368
Number of pages5
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
StatePublished - 1 Apr 2003
EventStatphys - Taiwan - 2002: Lattice Models and Complex Systems - Taipei and Taichung, Taiwan
Duration: 26 May 20021 Jun 2002


  • GOE
  • Hessian
  • Level statistics
  • Random matrices


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