Phonon Modes in Supercritical Fluids

Phonons, which are collective vibrational excitations of atoms in a periodic lattice, can be described by

the normal mode of vibrations, and their dispersion can be determined through analysis of these modes.

Extending such an analysis to liquids is challenging due to the diffusive motion of atoms and the lack of

periodic structure in liquids. Theories of time correlation functions have been employed in the past to

describe the collective motion of atoms in liquids, and dispersion relationships can be extracted from

the Fourier spectra of these correlation functions. In this work, we present a direct method of

extracting phonon dispersion from the elementary excitations using the ratio of zero-time correlations

of acceleration and velocity modes. By applying it to supercritical fluids below the Frenkel line, where

solid-like characteristics are prominent, we show that the dispersion relations obtained through our

method agree with those obtained using current time correlation functions. We then determine the

speed of sound using the dispersion of longitudinal and transverse phonon modes.