THE RELATIONSHIP BETWEEN THE ELASTIC-CONSTANTS AND THE INSTANTANEOUS NORMAL-MODES OF LIQUIDS

In the solid state the elastic properties of a substance are related q uite simply and directly to its phonon spectrum. However, while it is well-known that liquids possess certain macroscopic elastic properties , their relationship with an analogous set of liquid phonons is Far mo re tenuous. We show here that one candidate for what one might call th e phonons of a liquid-its instantaneous normal modes-has a very precis e connection with the liquid's high-Frequency macroscopic elastic modu li. This connection suggests, moreover, that there is at least some pl ane-wave-like character to the short-time, long-wavelength dynamics of liquids.