The relationship between the elastic constants and the instantaneous normal modes of liquids

In the solid st-ate tile elastic properties of a substance are related quil-e sinlply and directly to its phonon spectrum. However, while it is well-known that liqtlids possess certain macroscopic elastic properties, their relationship with an tinah/gotlS set of liquid pllonons is 1]_t1" more tentlotis. We show here that one candidate I~)r what one might cull the phonons of a liquid its instailtaneous ilOril~al rhodes has a very precise conllectioll with the liquidʹs high-17equency nlacroscopic elastic moduli. This ct)nlleCl-ion suggests, illoreover, that there is at least some plane-wave-like character to tile short-l-ime, long-wavelength dynamics of liquids.