Spectral statistics of instantaneous normal modes in liquids and random matrices

Srikanth Sastry, Nivedita Deo, and Silvio Franz
Phys. Rev. E 64, 016305 – Published 15 June 2001
PDFExport Citation

Abstract

We study the statistical properties of eigenvalues of the Hessian matrix H (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models. The eigenvalue spectra (the instantaneous normal mode or INM spectra) are evaluated numerically for configurations generated by molecular dynamics simulations. We find that distribution of spacings between nearest-neighbor eigenvalues, s, obeys quite well the Wigner prediction sexp(s2), with the agreement being better for higher densities at fixed temperature. The deviations display a correlation with the number of localized eigenstates (normal modes) in the liquid; there are fewer localized states at higher densities that we quantify by calculating the participation ratios of the normal modes. We confirm this observation by calculating the spacing distribution for parts of the INM spectra with high participation ratios, obtaining greater conformity with the Wigner form. We also calculate the spectral rigidity and find a substantial dependence on the density of the liquid.

  • Received 29 October 2000

DOI:https://doi.org/10.1103/PhysRevE.64.016305

©2001 American Physical Society

Authors & Affiliations

Srikanth Sastry1,*, Nivedita Deo1,3,4,†, and Silvio Franz2,‡

  • 1Jawaharlal Nehru Center for Advanced Scientific Research, Bangalore 560064, India
  • 2The Adbus Salam International Centre for Theoretical Physics, Treieste, Italy
  • 3Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501
  • 4Poornaprajna Institute for Scientific Research, Sadashivanagar, Bangalore 560080, India

  • *Email address: sastry@jncasr.ac.in
  • Email address: ndeo@vsnl.net
  • Email address: franz@ictp.trieste.it

References (Subscription Required)

Click to Expand
Issue

Vol. 64, Iss. 1 — July 2001

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×