Spectral statistics of instantaneous normal modes in liquids and random matrices - art. no. 016305

We study the statistical properties of eigenvalues of the Hessian matrix H (matrix of second derivatives of the potential energy) for a classical atom ic liquid, and compare these properties with predictions for random matrix models. The eigenvalue spectra (the instantaneous normal mode or INM spectr al are evaluated numerically for configurations generated by molecular dyna mics simulations. We find that distribution of spacings between nearest-nei ghbor eigenvalues, s, obeys quite well the Wigner prediction s exp(-s(2)), with the agree ment being better for higher densities at fixed temperature. The deviations display a correlation with the number of localized eigensta tes (normal modes) in the liquid; there are fewer localized states at highe r densities that we quantify by calculating the participation ratios of the normal modes. We confirm this observation by calculating the spacing distr ibution for parts of the INM spectra with high participation ratios, obtain ing greater conformity with the Wigner form. We also calculate the spectral rigidity and find a substantial dependence on the density of the liquid.